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    <link:label id="lab_us-gaap_IPOMember_019c12b4-622c-726c-8768-64fc89cd47f9_terseLabel_en-US" xlink:label="lab_us-gaap_IPOMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">IPO</link:label>
    <link:label id="lab_us-gaap_IPOMember_label_en-US" xlink:label="lab_us-gaap_IPOMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">IPO [Member]</link:label>
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    <link:label id="lab_ecd_TabularListTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tabular List, Table</link:label>
    <link:label id="lab_ecd_TabularListTableTextBlock_label_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tabular List [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_019c0e48-043b-7d9f-96c0-875517103ed3_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recently Adopted Accounting Pronouncements and Recently Issued Accounting Pronouncements Not Yet Adopted</link:label>
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    <link:label id="lab_blln_LesseeOperatingLeaseLeaseNotYetCommencedInitialAnnualRentalRate_019c094f-810c-7eb7-b8b9-760c00ad075d_terseLabel_en-US" xlink:label="lab_blln_LesseeOperatingLeaseLeaseNotYetCommencedInitialAnnualRentalRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Initial rental rate</link:label>
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    <link:label id="lab_blln_LesseeOperatingLeaseLeaseNotYetCommencedInitialAnnualRentalRate_documentation_en-US" xlink:label="lab_blln_LesseeOperatingLeaseLeaseNotYetCommencedInitialAnnualRentalRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Lease Not yet Commenced, Initial Annual Rental Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_LesseeOperatingLeaseLeaseNotYetCommencedInitialAnnualRentalRate" xlink:href="blln-20251231.xsd#blln_LesseeOperatingLeaseLeaseNotYetCommencedInitialAnnualRentalRate"/>
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    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByBalanceSheetGroupingTextBlock"/>
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    <link:label id="lab_us-gaap_IncomeTaxReconciliationTaxCreditsResearch_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationTaxCreditsResearch" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Tax Credit, Research, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationTaxCreditsResearch" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationTaxCreditsResearch"/>
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    <link:label id="lab_ecd_AdjToCompAxis_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation:</link:label>
    <link:label id="lab_ecd_AdjToCompAxis_label_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToCompAxis"/>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_019c124f-2694-7316-ac88-db5ea59d1d51_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transactions</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions Disclosure [Text Block]</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock, Class of Stock [Table]</link:label>
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    <link:label id="lab_ecd_AdjToCompAmt_label_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation Amount</link:label>
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    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_019c65f2-2fef-7e82-9117-4cd83d13475d_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation</link:label>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConsolidationPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:to="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensation_019c0d23-93a6-75ee-9836-60c1979e4a94_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock-based compensation</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Noncash Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensation" xlink:to="lab_us-gaap_ShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_019c139b-2737-7523-b394-45c1c0da5494_verboseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Employee Stock Option</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_019c124b-3c67-7f96-91b9-432827b808be_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding stock options</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_019c09f6-68af-7406-9f13-2d86f3cd8640_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Property, Plant and Equipment [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfPropertyPlantAndEquipmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:to="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock_019c0e15-6017-70aa-8903-cffb089f2ad0_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:to="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract_019c65d1-534e-7f7a-becc-d2c5c2d19394_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percent</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Percent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_019c124b-3c67-704a-bcd1-141ff76928a7_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_019c0c7d-352a-7a1b-9c6d-2573633820ec_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total stockholders&#8217; equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_019c0cdd-5616-75d7-aa30-fbd7394e90fa_periodStartLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_019c0cdd-5616-7c67-987a-4298ee804e46_periodEndLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingPoliciesProcLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_InsiderTradingPoliciesProcLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:to="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTextBlock_019c09f5-050e-73f4-b127-3d7a539833d4_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Property and Equipment Net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTextBlock_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_019c0c7d-352a-76e5-a3bd-9ff3a2fab77b_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesAuthorized" xlink:to="lab_us-gaap_CommonStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_DebtInstrumentCovenantTrailingSixMonthWorldwideNetRevenueMinimum_019c8fff-5ba2-704a-a2dc-f727097b4009_verboseLabel_en-US" xlink:label="lab_blln_DebtInstrumentCovenantTrailingSixMonthWorldwideNetRevenueMinimum" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Worldwide net revenue</link:label>
    <link:label id="lab_blln_DebtInstrumentCovenantTrailingSixMonthWorldwideNetRevenueMinimum_019c12bb-9e5a-70be-bb15-a6bb121a5536_terseLabel_en-US" xlink:label="lab_blln_DebtInstrumentCovenantTrailingSixMonthWorldwideNetRevenueMinimum" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum Trailing Six-Month Net Revenue Threshold (in millions)</link:label>
    <link:label id="lab_blln_DebtInstrumentCovenantTrailingSixMonthWorldwideNetRevenueMinimum_label_en-US" xlink:label="lab_blln_DebtInstrumentCovenantTrailingSixMonthWorldwideNetRevenueMinimum" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Covenant, Trailing Six-Month Worldwide Net Revenue, Minimum</link:label>
    <link:label id="lab_blln_DebtInstrumentCovenantTrailingSixMonthWorldwideNetRevenueMinimum_documentation_en-US" xlink:label="lab_blln_DebtInstrumentCovenantTrailingSixMonthWorldwideNetRevenueMinimum" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Covenant, Trailing Six-Month Worldwide Net Revenue, Minimum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_DebtInstrumentCovenantTrailingSixMonthWorldwideNetRevenueMinimum" xlink:href="blln-20251231.xsd#blln_DebtInstrumentCovenantTrailingSixMonthWorldwideNetRevenueMinimum"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_DebtInstrumentCovenantTrailingSixMonthWorldwideNetRevenueMinimum" xlink:to="lab_blln_DebtInstrumentCovenantTrailingSixMonthWorldwideNetRevenueMinimum" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_019c1e5b-3822-74f8-848c-4bfaba4eefa5_verboseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common stock in connection with initial public offering, net of underwriting discounts and commissions and issuance costs (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_DebtInstrumentRedemptionInternalRateOfReturnGenerated_019c12bb-9e5a-74b3-a7de-616fa4d00158_terseLabel_en-US" xlink:label="lab_blln_DebtInstrumentRedemptionInternalRateOfReturnGenerated" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redemption, internal rate of return generated</link:label>
    <link:label id="lab_blln_DebtInstrumentRedemptionInternalRateOfReturnGenerated_label_en-US" xlink:label="lab_blln_DebtInstrumentRedemptionInternalRateOfReturnGenerated" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Internal Rate Of Return Generated</link:label>
    <link:label id="lab_blln_DebtInstrumentRedemptionInternalRateOfReturnGenerated_documentation_en-US" xlink:label="lab_blln_DebtInstrumentRedemptionInternalRateOfReturnGenerated" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Internal Rate Of Return Generated</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_DebtInstrumentRedemptionInternalRateOfReturnGenerated" xlink:href="blln-20251231.xsd#blln_DebtInstrumentRedemptionInternalRateOfReturnGenerated"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_DebtInstrumentRedemptionInternalRateOfReturnGenerated" xlink:to="lab_blln_DebtInstrumentRedemptionInternalRateOfReturnGenerated" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_AccruedFixedAssetPurchasesCurrent_019c07d9-7d56-7ffa-befa-3fe77d65095c_terseLabel_en-US" xlink:label="lab_blln_AccruedFixedAssetPurchasesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued fixed asset purchases</link:label>
    <link:label id="lab_blln_AccruedFixedAssetPurchasesCurrent_label_en-US" xlink:label="lab_blln_AccruedFixedAssetPurchasesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Fixed Asset Purchases, Current</link:label>
    <link:label id="lab_blln_AccruedFixedAssetPurchasesCurrent_documentation_en-US" xlink:label="lab_blln_AccruedFixedAssetPurchasesCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accrued Fixed Asset Purchases, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_AccruedFixedAssetPurchasesCurrent" xlink:href="blln-20251231.xsd#blln_AccruedFixedAssetPurchasesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_AccruedFixedAssetPurchasesCurrent" xlink:to="lab_blln_AccruedFixedAssetPurchasesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_The2018PlanMember_019c139b-2737-78ef-87f9-3dfa5fae02c2_terseLabel_en-US" xlink:label="lab_blln_The2018PlanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">The 2018 Plan</link:label>
    <link:label id="lab_blln_The2018PlanMember_label_en-US" xlink:label="lab_blln_The2018PlanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">The 2018 Plan [Member]</link:label>
    <link:label id="lab_blln_The2018PlanMember_documentation_en-US" xlink:label="lab_blln_The2018PlanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The 2018 Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_The2018PlanMember" xlink:href="blln-20251231.xsd#blln_The2018PlanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_The2018PlanMember" xlink:to="lab_blln_The2018PlanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskCreditRisk_019c0e16-90cf-710b-bfe8-9107d177ab7a_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskCreditRisk" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration of Credit Risk</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskCreditRisk_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskCreditRisk" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk, Credit Risk, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskCreditRisk" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskCreditRisk"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskCreditRisk" xlink:to="lab_us-gaap_ConcentrationRiskCreditRisk" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_019c0c7d-352a-73ac-ad2b-767595ea554c_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities, redeemable convertible preferred stock, and stockholders&#8217; deficit</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StateAndLocalJurisdictionMember_019c0e8f-e36a-70a0-bf69-35e0743976d6_terseLabel_en-US" xlink:label="lab_us-gaap_StateAndLocalJurisdictionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">State and Local Jurisdiction</link:label>
    <link:label id="lab_us-gaap_StateAndLocalJurisdictionMember_label_en-US" xlink:label="lab_us-gaap_StateAndLocalJurisdictionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">State and Local Jurisdiction [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StateAndLocalJurisdictionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StateAndLocalJurisdictionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StateAndLocalJurisdictionMember" xlink:to="lab_us-gaap_StateAndLocalJurisdictionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CoverAbstract_label_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CoverAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CoverAbstract" xlink:to="lab_dei_CoverAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure_019c0a42-e665-74cc-957c-9f66b4d0eb5e_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Money market funds</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:to="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConversionOfStockNameDomain_019c6591-5ff0-7415-aa82-1ddf6ac057ff_terseLabel_en-US" xlink:label="lab_us-gaap_ConversionOfStockNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion of Stock, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_ConversionOfStockNameDomain_label_en-US" xlink:label="lab_us-gaap_ConversionOfStockNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Conversion of Stock, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConversionOfStockNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConversionOfStockNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConversionOfStockNameDomain" xlink:to="lab_us-gaap_ConversionOfStockNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MaximumMember_019c0a53-052e-7004-85fb-4f6f46c274e6_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum</link:label>
    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MaximumMember" xlink:to="lab_srt_MaximumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_SeriesA3RedeemableConvertiblePreferredStockMember_019c0887-a6e4-790e-8b21-0a5b8c30b3a5_terseLabel_en-US" xlink:label="lab_blln_SeriesA3RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series A-3</link:label>
    <link:label id="lab_blln_SeriesA3RedeemableConvertiblePreferredStockMember_label_en-US" xlink:label="lab_blln_SeriesA3RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series A-3 Redeemable Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_blln_SeriesA3RedeemableConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_blln_SeriesA3RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series A-3 Redeemable Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_SeriesA3RedeemableConvertiblePreferredStockMember" xlink:href="blln-20251231.xsd#blln_SeriesA3RedeemableConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_SeriesA3RedeemableConvertiblePreferredStockMember" xlink:to="lab_blln_SeriesA3RedeemableConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedStockMember_019c6625-9fe7-7834-89fa-602680a1d5e2_verboseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Restricted stock</link:label>
    <link:label id="lab_us-gaap_RestrictedStockMember_019c124b-3c67-7ff0-8414-80e426a0bf2f_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted stock awards in exchange for non-recourse note</link:label>
    <link:label id="lab_us-gaap_RestrictedStockMember_label_en-US" xlink:label="lab_us-gaap_RestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedStockMember" xlink:to="lab_us-gaap_RestrictedStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonPeoNeoAvgTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:to="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_019c1285-31dd-723f-afd8-b32cc5165e1b_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentLineItems" xlink:to="lab_us-gaap_DebtInstrumentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019c139b-2737-7196-8992-4cc79fa8eec1_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:to="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues_019c0cdd-5616-73c6-978b-9ed860fbf0ad_terseLabel_en-US" xlink:label="lab_blln_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of redeemable convertible preferred stock, net of issuance costs (in shares)</link:label>
    <link:label id="lab_blln_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues_label_en-US" xlink:label="lab_blln_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Stock Issued During Period, Shares, New Issues</link:label>
    <link:label id="lab_blln_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues_documentation_en-US" xlink:label="lab_blln_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Stock Issued During Period, Shares, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues" xlink:href="blln-20251231.xsd#blln_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues" xlink:to="lab_blln_TemporaryEquityStockIssuedDuringPeriodSharesNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote</link:label>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToNonPeoNeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:to="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CompensationAndRetirementDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CompensationAndRetirementDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retirement Benefits [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CompensationAndRetirementDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CompensationAndRetirementDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CompensationAndRetirementDisclosureAbstract" xlink:to="lab_us-gaap_CompensationAndRetirementDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodOneMember_019c12bb-9e5a-732f-810e-58606faa0114_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period One</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodOneMember_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodOneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period One [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodOneMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPeriodOneMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPeriodOneMember" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPeriodOneMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityLineItems_019c0811-1015-77b3-8dd5-ee86a479b9c5_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Temporary Equity [Line Items]</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityLineItems_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityLineItems" xlink:to="lab_us-gaap_TemporaryEquityLineItems" xlink:type="arc" order="1"/>
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    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonRule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:to="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019c0c8b-30ae-7412-9ba5-e198d23f2ed3_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income (loss) before provision for income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityShellCompany_019c0cb2-8c5f-75d4-b14b-e5bfd14e1c7b_terseLabel_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:label id="lab_dei_EntityShellCompany_label_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityShellCompany" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityShellCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityShellCompany" xlink:to="lab_dei_EntityShellCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_OptionsToPurchaseCommonStockMember_019c139b-2737-7fd5-a297-fc49ceb36e3c_terseLabel_en-US" xlink:label="lab_blln_OptionsToPurchaseCommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Options to purchase common stock</link:label>
    <link:label id="lab_blln_OptionsToPurchaseCommonStockMember_label_en-US" xlink:label="lab_blln_OptionsToPurchaseCommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Options To Purchase Common Stock [Member]</link:label>
    <link:label id="lab_blln_OptionsToPurchaseCommonStockMember_documentation_en-US" xlink:label="lab_blln_OptionsToPurchaseCommonStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Options To Purchase Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_OptionsToPurchaseCommonStockMember" xlink:href="blln-20251231.xsd#blln_OptionsToPurchaseCommonStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_OptionsToPurchaseCommonStockMember" xlink:to="lab_blln_OptionsToPurchaseCommonStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTable_019c1285-31dd-7ed4-808c-abadd92c900b_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTable_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTable" xlink:to="lab_us-gaap_DebtInstrumentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfDebt_019c0d23-93a7-7a1e-b1ee-4ce870e26e5f_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from issuance of debt, net</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromIssuanceOfDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfDebt" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock_019c4d4d-aaa9-7f8b-aa48-329e37742bbb_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Income Taxes Paid</link:label>
    <link:label id="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Cash Flow, Supplemental Disclosures [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgMnpiCnsdrdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:to="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTextBlock_019c139b-2737-7367-bff4-81b6633dddd9_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Stock-Based Compensation Expense</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Expensed and Capitalized, Amount [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTextBlock"/>
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    <link:label id="lab_us-gaap_OperatingLeaseLiabilityCurrent_019c0c7d-352a-7283-93bb-685d0cc68347_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease liabilities, current</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityCurrent_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilityCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilityCurrent" xlink:to="lab_us-gaap_OperatingLeaseLiabilityCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseAbstract_019c7791-9b61-7e4e-be4a-cf7760eba210_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nontaxable or nondeductible items</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseAbstract_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Percent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseAbstract"/>
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    <link:label id="lab_us-gaap_FinanceLeaseInterestExpense_019c08e0-1031-737f-9ac6-c6211cabf8a2_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseInterestExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating cash flows from financing leases (interest paid):</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseInterestExpense_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseInterestExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Interest Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseInterestExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseInterestExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseInterestExpense" xlink:to="lab_us-gaap_FinanceLeaseInterestExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_FairValueAdjustmentOfTermLoanIncludingInterest_019c0c8b-30ae-7fc0-a9c9-056795c409ff_terseLabel_en-US" xlink:label="lab_blln_FairValueAdjustmentOfTermLoanIncludingInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of term loan</link:label>
    <link:label id="lab_blln_FairValueAdjustmentOfTermLoanIncludingInterest_label_en-US" xlink:label="lab_blln_FairValueAdjustmentOfTermLoanIncludingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Adjustment of Term Loan, Including Interest</link:label>
    <link:label id="lab_blln_FairValueAdjustmentOfTermLoanIncludingInterest_documentation_en-US" xlink:label="lab_blln_FairValueAdjustmentOfTermLoanIncludingInterest" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value Adjustment of Term Loan, Including Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_FairValueAdjustmentOfTermLoanIncludingInterest" xlink:href="blln-20251231.xsd#blln_FairValueAdjustmentOfTermLoanIncludingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_FairValueAdjustmentOfTermLoanIncludingInterest" xlink:to="lab_blln_FairValueAdjustmentOfTermLoanIncludingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAccountsPayableAndAccruedLiabilities_019c0c7d-352a-7b9d-8859-42850fe1ba1e_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAccountsPayableAndAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses and other current liabilities</link:label>
    <link:label id="lab_us-gaap_OtherAccountsPayableAndAccruedLiabilities_label_en-US" xlink:label="lab_us-gaap_OtherAccountsPayableAndAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Accounts Payable and Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAccountsPayableAndAccruedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAccountsPayableAndAccruedLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAccountsPayableAndAccruedLiabilities" xlink:to="lab_us-gaap_OtherAccountsPayableAndAccruedLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember_019c6601-5093-79fd-96d9-a6b1a8b1a215_terseLabel_en-US" xlink:label="lab_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Computer software</link:label>
    <link:label id="lab_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember_label_en-US" xlink:label="lab_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Software and Software Development Costs [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SoftwareAndSoftwareDevelopmentCostsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember" xlink:to="lab_us-gaap_SoftwareAndSoftwareDevelopmentCostsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_019c0cb2-8c5f-71b2-9e18-2378b3a740d6_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalPeriodFocus" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFiscalPeriodFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalPeriodFocus" xlink:to="lab_dei_DocumentFiscalPeriodFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquitySharesAuthorized_019c0c7d-352a-70bd-b0c2-df1b6d54b838_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redeemable convertible preferred stock, authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesAuthorized_019c0811-1015-7e5a-a612-37be40d33ce9_verboseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Shares Authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesAuthorized_label_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquitySharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquitySharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquitySharesAuthorized" xlink:to="lab_us-gaap_TemporaryEquitySharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Method</link:label>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMethodTextBlock" xlink:to="lab_ecd_AwardTmgMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FurnitureAndFixturesMember_019c09f6-68af-726a-8ce0-c2c9588e5a18_terseLabel_en-US" xlink:label="lab_us-gaap_FurnitureAndFixturesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Furniture and fixtures</link:label>
    <link:label id="lab_us-gaap_FurnitureAndFixturesMember_label_en-US" xlink:label="lab_us-gaap_FurnitureAndFixturesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Furniture and Fixtures [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FurnitureAndFixturesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FurnitureAndFixturesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FurnitureAndFixturesMember" xlink:to="lab_us-gaap_FurnitureAndFixturesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AwardTypeAxis_019c12f0-5fa0-7912-9874-33c67a8bd581_terseLabel_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type</link:label>
    <link:label id="lab_us-gaap_AwardTypeAxis_label_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AwardTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AwardTypeAxis" xlink:to="lab_us-gaap_AwardTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityNoncurrent_019ca097-4040-7c2b-a59c-889e28d555ad_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred revenue, non-current</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityNoncurrent_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Liability, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerLiabilityNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractWithCustomerLiabilityNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerLiabilityNoncurrent" xlink:to="lab_us-gaap_ContractWithCustomerLiabilityNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_ChiefTechnologyOfficerAndCoFounderMember_019c139b-2737-7cfc-88bf-7b5bbe87ef21_terseLabel_en-US" xlink:label="lab_blln_ChiefTechnologyOfficerAndCoFounderMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Chief Technology Officer And Co-Founder</link:label>
    <link:label id="lab_blln_ChiefTechnologyOfficerAndCoFounderMember_label_en-US" xlink:label="lab_blln_ChiefTechnologyOfficerAndCoFounderMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Chief Technology Officer And Co-Founder [Member]</link:label>
    <link:label id="lab_blln_ChiefTechnologyOfficerAndCoFounderMember_documentation_en-US" xlink:label="lab_blln_ChiefTechnologyOfficerAndCoFounderMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Chief Technology Officer And Co-Founder</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_ChiefTechnologyOfficerAndCoFounderMember" xlink:href="blln-20251231.xsd#blln_ChiefTechnologyOfficerAndCoFounderMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_ChiefTechnologyOfficerAndCoFounderMember" xlink:to="lab_blln_ChiefTechnologyOfficerAndCoFounderMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_019c0e45-cd6f-7381-9e2a-1d3d79c0d59c_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock-Based Compensation</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:to="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_TradingSymbol_019c0cb2-8c5f-792d-9308-68a361d28ba6_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:label id="lab_dei_TradingSymbol_label_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_TradingSymbol"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_TradingSymbol" xlink:to="lab_dei_TradingSymbol" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_019c08c3-73bc-767e-b5bc-8ba9da87383f_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance_019c65ce-3834-7e89-af9b-c4c7fbc6a745_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in valuation allowance</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Change in Deferred Tax Assets Valuation Allowance, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_019c0cb2-8c5f-7bfe-8ba2-d5660b1858bc_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent_019c0970-ad28-7df4-8b94-24f492514c08_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance lease, weighted average discount rate, percent</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Weighted Average Discount Rate, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:to="lab_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsFairValueOfCommonStock_019c139b-2737-7ae7-8e92-eb5ffab0edf3_terseLabel_en-US" xlink:label="lab_blln_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsFairValueOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of common stock (in dollars per share)</link:label>
    <link:label id="lab_blln_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsFairValueOfCommonStock_label_en-US" xlink:label="lab_blln_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsFairValueOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement By Share-Based Payment Award, Fair Value Assumptions, Fair Value Of Common Stock</link:label>
    <link:label id="lab_blln_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsFairValueOfCommonStock_documentation_en-US" xlink:label="lab_blln_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsFairValueOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement By Share-Based Payment Award, Fair Value Assumptions, Fair Value Of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsFairValueOfCommonStock" xlink:href="blln-20251231.xsd#blln_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsFairValueOfCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsFairValueOfCommonStock" xlink:to="lab_blln_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsFairValueOfCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_TemporaryEquityLiquidationPreferencePerShareMultiplier_019ca028-b3bb-7057-91d8-f961ddd7fd1c_terseLabel_en-US" xlink:label="lab_blln_TemporaryEquityLiquidationPreferencePerShareMultiplier" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liquidation preference, multiplier</link:label>
    <link:label id="lab_blln_TemporaryEquityLiquidationPreferencePerShareMultiplier_label_en-US" xlink:label="lab_blln_TemporaryEquityLiquidationPreferencePerShareMultiplier" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Liquidation Preference Per Share, Multiplier</link:label>
    <link:label id="lab_blln_TemporaryEquityLiquidationPreferencePerShareMultiplier_documentation_en-US" xlink:label="lab_blln_TemporaryEquityLiquidationPreferencePerShareMultiplier" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Liquidation Preference Per Share, Multiplier</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_TemporaryEquityLiquidationPreferencePerShareMultiplier" xlink:href="blln-20251231.xsd#blln_TemporaryEquityLiquidationPreferencePerShareMultiplier"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_TemporaryEquityLiquidationPreferencePerShareMultiplier" xlink:to="lab_blln_TemporaryEquityLiquidationPreferencePerShareMultiplier" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonPeoNeoAvgCompActuallyPaidAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:to="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementLocationDomain_019c139b-2738-7e12-8ad9-8b18297c1560_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Income Location, Balance [Domain]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementLocationDomain_label_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Income Location, Balance [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementLocationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementLocationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementLocationDomain" xlink:to="lab_us-gaap_IncomeStatementLocationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_019c1403-7276-7388-a198-a20e6b5152c8_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Stock Units (RSUs)</link:label>
    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_019c660e-7621-7969-9e9d-2c9be1a29f7a_verboseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Restricted stock units outstanding</link:label>
    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_label_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock Units (RSUs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockUnitsRSUMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedStockUnitsRSUMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedStockUnitsRSUMember" xlink:to="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsOtherMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_SeriesCRedeemableConvertiblePreferredStockMember_019c0887-a6e4-7610-9a90-b3a509e81ce7_terseLabel_en-US" xlink:label="lab_blln_SeriesCRedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series C</link:label>
    <link:label id="lab_blln_SeriesCRedeemableConvertiblePreferredStockMember_label_en-US" xlink:label="lab_blln_SeriesCRedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series C Redeemable Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_blln_SeriesCRedeemableConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_blln_SeriesCRedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series C Redeemable Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_SeriesCRedeemableConvertiblePreferredStockMember" xlink:href="blln-20251231.xsd#blln_SeriesCRedeemableConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_SeriesCRedeemableConvertiblePreferredStockMember" xlink:to="lab_blln_SeriesCRedeemableConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_Q12026Member_019c12bb-9e5a-71b8-a2f1-085049e586b3_terseLabel_en-US" xlink:label="lab_blln_Q12026Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Q1 2026</link:label>
    <link:label id="lab_blln_Q12026Member_label_en-US" xlink:label="lab_blln_Q12026Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Q1 2026 [Member]</link:label>
    <link:label id="lab_blln_Q12026Member_documentation_en-US" xlink:label="lab_blln_Q12026Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Q1 2026</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_Q12026Member" xlink:href="blln-20251231.xsd#blln_Q12026Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_Q12026Member" xlink:to="lab_blln_Q12026Member" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_019c0cb2-8c5f-7a23-b7e4-f947b5099e0e_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_label_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityEmergingGrowthCompany" xlink:to="lab_dei_EntityEmergingGrowthCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireIntangibleAssets_019c1e60-b50b-7a97-a11d-305084d50431_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireIntangibleAssets" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchase of domain name</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireIntangibleAssets_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Intangible Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireIntangibleAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireIntangibleAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireIntangibleAssets" xlink:to="lab_us-gaap_PaymentsToAcquireIntangibleAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_PaymentsForRevenueParticipationAgreement_019c12bb-9e5a-78a4-bc10-65e626c5774d_terseLabel_en-US" xlink:label="lab_blln_PaymentsForRevenueParticipationAgreement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payments for revenue participation agreement</link:label>
    <link:label id="lab_blln_PaymentsForRevenueParticipationAgreement_label_en-US" xlink:label="lab_blln_PaymentsForRevenueParticipationAgreement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments For Revenue Participation Agreement</link:label>
    <link:label id="lab_blln_PaymentsForRevenueParticipationAgreement_documentation_en-US" xlink:label="lab_blln_PaymentsForRevenueParticipationAgreement" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments For Revenue Participation Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_PaymentsForRevenueParticipationAgreement" xlink:href="blln-20251231.xsd#blln_PaymentsForRevenueParticipationAgreement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_PaymentsForRevenueParticipationAgreement" xlink:to="lab_blln_PaymentsForRevenueParticipationAgreement" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_ConversionOfWarrantsMember_019c65a2-cbb8-7b26-b3ce-bfe9e546aad6_terseLabel_en-US" xlink:label="lab_blln_ConversionOfWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion Of Warrants</link:label>
    <link:label id="lab_blln_ConversionOfWarrantsMember_label_en-US" xlink:label="lab_blln_ConversionOfWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Conversion Of Warrants [Member]</link:label>
    <link:label id="lab_blln_ConversionOfWarrantsMember_documentation_en-US" xlink:label="lab_blln_ConversionOfWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Conversion Of Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_ConversionOfWarrantsMember" xlink:href="blln-20251231.xsd#blln_ConversionOfWarrantsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_ConversionOfWarrantsMember" xlink:to="lab_blln_ConversionOfWarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1_019c0971-0e7b-71e3-8a77-8fbf1663e80e_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance lease, weighted average remaining lease term</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Weighted Average Remaining Lease Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:to="lab_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_019c139b-2737-7f02-92a7-1c3401c516bf_periodStartLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_019c139b-2737-7478-93ad-523c6cdbc132_periodEndLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year</link:label>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:to="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedInsuranceCurrent_019c07e4-0466-7f87-bbf1-474f16d1849a_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedInsuranceCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued insurance expenses</link:label>
    <link:label id="lab_us-gaap_AccruedInsuranceCurrent_label_en-US" xlink:label="lab_us-gaap_AccruedInsuranceCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Insurance, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedInsuranceCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccruedInsuranceCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedInsuranceCurrent" xlink:to="lab_us-gaap_AccruedInsuranceCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases_019c0e75-67bf-7556-bd5f-2fd9bad16fdd_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additions</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Purchases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount_019c08d7-8527-7da7-8d97-b6af3d46c46f_negatedLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Less: interest expense</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, Undiscounted Excess Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount" xlink:to="lab_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019c08a4-7a3c-7fea-ac8d-376c222bc370_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019c0cdd-5616-75ae-99d0-f8f8576eec16_periodStartLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019c0cdd-5616-7044-acfb-214fbb6a7723_periodEndLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesOutstanding" xlink:to="lab_us-gaap_CommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ChiefExecutiveOfficerMember_019c12b7-6afc-70ca-bc2a-054b32ef41df_terseLabel_en-US" xlink:label="lab_srt_ChiefExecutiveOfficerMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Chief Executive Officer</link:label>
    <link:label id="lab_srt_ChiefExecutiveOfficerMember_label_en-US" xlink:label="lab_srt_ChiefExecutiveOfficerMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Chief Executive Officer [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ChiefExecutiveOfficerMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ChiefExecutiveOfficerMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ChiefExecutiveOfficerMember" xlink:to="lab_srt_ChiefExecutiveOfficerMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromRelatedPartyDebt_019cb8ee-724c-7f44-8002-bd697d2763bc_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromRelatedPartyDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from repayment of promissory notes by executives</link:label>
    <link:label id="lab_us-gaap_ProceedsFromRelatedPartyDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromRelatedPartyDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Related Party Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromRelatedPartyDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromRelatedPartyDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromRelatedPartyDebt" xlink:to="lab_us-gaap_ProceedsFromRelatedPartyDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_DebtCovenantTrancheTwoMember_019c12bb-9e5a-7b49-ada9-e7a7c3217f94_terseLabel_en-US" xlink:label="lab_blln_DebtCovenantTrancheTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Second Tranche</link:label>
    <link:label id="lab_blln_DebtCovenantTrancheTwoMember_label_en-US" xlink:label="lab_blln_DebtCovenantTrancheTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Covenant, Tranche Two [Member]</link:label>
    <link:label id="lab_blln_DebtCovenantTrancheTwoMember_documentation_en-US" xlink:label="lab_blln_DebtCovenantTrancheTwoMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Covenant, Tranche Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_DebtCovenantTrancheTwoMember" xlink:href="blln-20251231.xsd#blln_DebtCovenantTrancheTwoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_DebtCovenantTrancheTwoMember" xlink:to="lab_blln_DebtCovenantTrancheTwoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract_019c0e76-2c67-78b7-a9ec-9a215a87c53a_terseLabel_en-US" xlink:label="lab_us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current:</link:label>
    <link:label id="lab_us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract_label_en-US" xlink:label="lab_us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Income Tax Expense (Benefit), Continuing Operations [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:to="lab_us-gaap_CurrentIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_WarrantsFairValueDisclosure_019c0a42-a2fd-74dd-b844-7d0bdab637a5_terseLabel_en-US" xlink:label="lab_blln_WarrantsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants</link:label>
    <link:label id="lab_blln_WarrantsFairValueDisclosure_label_en-US" xlink:label="lab_blln_WarrantsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrants, Fair Value Disclosure</link:label>
    <link:label id="lab_blln_WarrantsFairValueDisclosure_documentation_en-US" xlink:label="lab_blln_WarrantsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Warrants, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_WarrantsFairValueDisclosure" xlink:href="blln-20251231.xsd#blln_WarrantsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_WarrantsFairValueDisclosure" xlink:to="lab_blln_WarrantsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount_019c0e8f-e36a-7b2d-a435-ff663ddd9095_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additions/(reductions) recognized in income tax provision</link:label>
    <link:label id="lab_us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount_label_en-US" xlink:label="lab_us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Allowance, Deferred Tax Asset, Increase (Decrease), Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount" xlink:to="lab_us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_019c6578-9d66-7bac-b1d7-e7320436b65b_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common stock upon exercise of stock options</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Stock Options Exercised</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year</link:label>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_label_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:to="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_ThereafterMember_019c12bb-9e5a-776a-bf3d-8d100e82c59c_terseLabel_en-US" xlink:label="lab_blln_ThereafterMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_blln_ThereafterMember_label_en-US" xlink:label="lab_blln_ThereafterMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Thereafter [Member]</link:label>
    <link:label id="lab_blln_ThereafterMember_documentation_en-US" xlink:label="lab_blln_ThereafterMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_ThereafterMember" xlink:href="blln-20251231.xsd#blln_ThereafterMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_ThereafterMember" xlink:to="lab_blln_ThereafterMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrent_019c0c7d-352a-79a0-9f3e-98aab2d954ad_terseLabel_en-US" xlink:label="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepaid expenses and other current assets</link:label>
    <link:label id="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrent_label_en-US" xlink:label="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepaid Expense and Other Assets, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PrepaidExpenseAndOtherAssetsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xlink:to="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressPostalZipCode_019c0cb2-8c5f-7c56-94d0-b70b65eded5e_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressPostalZipCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressPostalZipCode" xlink:to="lab_dei_EntityAddressPostalZipCode" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDeterminationDate_terseLabel_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:label id="lab_ecd_RestatementDeterminationDate_label_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDeterminationDate" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RestatementDeterminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDeterminationDate" xlink:to="lab_ecd_RestatementDeterminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorizedPerParticipant_019c6617-6c93-7bfa-8162-0eb1b1b064ab_terseLabel_en-US" xlink:label="lab_blln_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorizedPerParticipant" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of shares authorized, per participant (in shares)</link:label>
    <link:label id="lab_blln_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorizedPerParticipant_label_en-US" xlink:label="lab_blln_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorizedPerParticipant" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Authorized, Per Participant</link:label>
    <link:label id="lab_blln_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorizedPerParticipant_documentation_en-US" xlink:label="lab_blln_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorizedPerParticipant" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Authorized, Per Participant</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorizedPerParticipant" xlink:href="blln-20251231.xsd#blln_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorizedPerParticipant"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorizedPerParticipant" xlink:to="lab_blln_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorizedPerParticipant" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_019c0c8b-30ae-7de2-b186-4525e841f228_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total provision for income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_019c0e76-2c67-734c-ae79-c93ebd4cab8a_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total provision for income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonClassBMember_019c0c82-11c8-7864-a0a4-e7132ec04d9b_terseLabel_en-US" xlink:label="lab_us-gaap_CommonClassBMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Class B</link:label>
    <link:label id="lab_us-gaap_CommonClassBMember_label_en-US" xlink:label="lab_us-gaap_CommonClassBMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Class B [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassBMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonClassBMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonClassBMember" xlink:to="lab_us-gaap_CommonClassBMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentInformationLineItems_019c0cb2-8c5f-733f-bb29-7576e4204dac_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Line Items]</link:label>
    <link:label id="lab_dei_DocumentInformationLineItems_label_en-US" xlink:label="lab_dei_DocumentInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentInformationLineItems" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentInformationLineItems" xlink:to="lab_dei_DocumentInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsSvcCstMember" xlink:to="lab_ecd_PnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_DebtCovenantTrancheFourMember_019c12bb-9e5a-7fcc-acaa-e9bb247ce692_terseLabel_en-US" xlink:label="lab_blln_DebtCovenantTrancheFourMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fourth Tranche</link:label>
    <link:label id="lab_blln_DebtCovenantTrancheFourMember_label_en-US" xlink:label="lab_blln_DebtCovenantTrancheFourMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Covenant, Tranche Four [Member]</link:label>
    <link:label id="lab_blln_DebtCovenantTrancheFourMember_documentation_en-US" xlink:label="lab_blln_DebtCovenantTrancheFourMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Covenant, Tranche Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_DebtCovenantTrancheFourMember" xlink:href="blln-20251231.xsd#blln_DebtCovenantTrancheFourMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_DebtCovenantTrancheFourMember" xlink:to="lab_blln_DebtCovenantTrancheFourMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_019c0a42-e665-7b31-a424-7b202875c625_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentGross_019c09f6-68af-75d9-9d78-6b3eb96499df_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property and equipment, gross</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentGross_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentGross" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityPolicyTextBlock_019ca01c-2b13-7541-b3ca-56071cdaceed_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redeemable Convertible Preferred Stock, Redeemable Convertible Preferred Stock Warrants and Common Stock Warrants</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stockholders' Equity, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityPolicyTextBlock" xlink:to="lab_us-gaap_StockholdersEquityPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotesPayableOtherPayablesMember_019c12bb-9e5a-787c-a6ba-fc0f1986aebe_terseLabel_en-US" xlink:label="lab_us-gaap_NotesPayableOtherPayablesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notes Payable</link:label>
    <link:label id="lab_us-gaap_NotesPayableOtherPayablesMember_label_en-US" xlink:label="lab_us-gaap_NotesPayableOtherPayablesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Payable, Other Payables [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotesPayableOtherPayablesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NotesPayableOtherPayablesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NotesPayableOtherPayablesMember" xlink:to="lab_us-gaap_NotesPayableOtherPayablesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_019c0d23-93a6-7bbf-8b4a-2e9c656b08f0_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of operating right-of-use assets</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset, Periodic Reduction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:to="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_LossOnExtinguishmentOfDebtPrepaymentFee_019c12bb-9e5a-72e2-a0fa-c3d6b8dda82f_terseLabel_en-US" xlink:label="lab_blln_LossOnExtinguishmentOfDebtPrepaymentFee" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepayment fee</link:label>
    <link:label id="lab_blln_LossOnExtinguishmentOfDebtPrepaymentFee_label_en-US" xlink:label="lab_blln_LossOnExtinguishmentOfDebtPrepaymentFee" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss on Extinguishment of Debt, Prepayment Fee</link:label>
    <link:label id="lab_blln_LossOnExtinguishmentOfDebtPrepaymentFee_documentation_en-US" xlink:label="lab_blln_LossOnExtinguishmentOfDebtPrepaymentFee" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loss on Extinguishment of Debt, Prepayment Fee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_LossOnExtinguishmentOfDebtPrepaymentFee" xlink:href="blln-20251231.xsd#blln_LossOnExtinguishmentOfDebtPrepaymentFee"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_LossOnExtinguishmentOfDebtPrepaymentFee" xlink:to="lab_blln_LossOnExtinguishmentOfDebtPrepaymentFee" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromStockOptionsExercised_019c0d23-93a7-756b-9629-dfed721528fb_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from exercise of stock options, net of repurchases</link:label>
    <link:label id="lab_us-gaap_ProceedsFromStockOptionsExercised_label_en-US" xlink:label="lab_us-gaap_ProceedsFromStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Stock Options Exercised</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromStockOptionsExercised" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromStockOptionsExercised"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromStockOptionsExercised" xlink:to="lab_us-gaap_ProceedsFromStockOptionsExercised" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxPaidFederalAfterRefundReceived_019c4d4e-be4b-7395-a6a8-e789c5bcc036_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidFederalAfterRefundReceived" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">US Federal</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPaidFederalAfterRefundReceived_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidFederalAfterRefundReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Paid, Federal, after Refund Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPaidFederalAfterRefundReceived" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPaidFederalAfterRefundReceived"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxPaidFederalAfterRefundReceived" xlink:to="lab_us-gaap_IncomeTaxPaidFederalAfterRefundReceived" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllTradingArrangementsMember_terseLabel_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Trading Arrangements</link:label>
    <link:label id="lab_ecd_AllTradingArrangementsMember_label_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Trading Arrangements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllTradingArrangementsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllTradingArrangementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllTradingArrangementsMember" xlink:to="lab_ecd_AllTradingArrangementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EqtyAwrdsAdjFnTextBlock"/>
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    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TotalShareholderRtnVsPeerGroupTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:to="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPricePercentage_019c12bb-9e5a-7384-ada8-504270fc0f29_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, redemption price, percentage</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPricePercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption Price, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPricePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageRemainingContractualTerm1_019c140c-23a5-7c22-b8f2-0c74dbb6df89_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageRemainingContractualTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average remaining contractual life, vested and expected to vest (in years)</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageRemainingContractualTerm1_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageRemainingContractualTerm1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Outstanding, Weighted Average Remaining Contractual Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageRemainingContractualTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageRemainingContractualTerm1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageRemainingContractualTerm1" xlink:to="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageRemainingContractualTerm1" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_LesseeOperatingLeaseLeaseNotYetCommencedAnnualRentIncreasePercentage_019c0953-2cc5-7275-8604-66a18130545a_terseLabel_en-US" xlink:label="lab_blln_LesseeOperatingLeaseLeaseNotYetCommencedAnnualRentIncreasePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Annual rent increases</link:label>
    <link:label id="lab_blln_LesseeOperatingLeaseLeaseNotYetCommencedAnnualRentIncreasePercentage_label_en-US" xlink:label="lab_blln_LesseeOperatingLeaseLeaseNotYetCommencedAnnualRentIncreasePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Lease Not yet Commenced, Annual Rent Increase, Percentage</link:label>
    <link:label id="lab_blln_LesseeOperatingLeaseLeaseNotYetCommencedAnnualRentIncreasePercentage_documentation_en-US" xlink:label="lab_blln_LesseeOperatingLeaseLeaseNotYetCommencedAnnualRentIncreasePercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Lease Not yet Commenced, Annual Rent Increase, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_LesseeOperatingLeaseLeaseNotYetCommencedAnnualRentIncreasePercentage" xlink:href="blln-20251231.xsd#blln_LesseeOperatingLeaseLeaseNotYetCommencedAnnualRentIncreasePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_LesseeOperatingLeaseLeaseNotYetCommencedAnnualRentIncreasePercentage" xlink:to="lab_blln_LesseeOperatingLeaseLeaseNotYetCommencedAnnualRentIncreasePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationOtherAdjustments_019c0e8b-a755-767f-b47a-829f14d3f771_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationOtherAdjustments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationOtherAdjustments_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationOtherAdjustments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Other Adjustments, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationOtherAdjustments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationOtherAdjustments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxReconciliationOtherAdjustments" xlink:to="lab_us-gaap_IncomeTaxReconciliationOtherAdjustments" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_LockUpAgreementNumberOfDays_019c8fa5-311c-7b07-8d7c-0fe144366c8a_terseLabel_en-US" xlink:label="lab_blln_LockUpAgreementNumberOfDays" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lock-up agreement, number of days</link:label>
    <link:label id="lab_blln_LockUpAgreementNumberOfDays_label_en-US" xlink:label="lab_blln_LockUpAgreementNumberOfDays" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lock-Up Agreement, Number of Days</link:label>
    <link:label id="lab_blln_LockUpAgreementNumberOfDays_documentation_en-US" xlink:label="lab_blln_LockUpAgreementNumberOfDays" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lock-Up Agreement, Number of Days</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_LockUpAgreementNumberOfDays" xlink:href="blln-20251231.xsd#blln_LockUpAgreementNumberOfDays"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_LockUpAgreementNumberOfDays" xlink:to="lab_blln_LockUpAgreementNumberOfDays" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncrementalCommonSharesAttributableToCallOptionsAndWarrants_019c124b-3c67-7290-8f0c-3ca3d90eb2be_terseLabel_en-US" xlink:label="lab_us-gaap_IncrementalCommonSharesAttributableToCallOptionsAndWarrants" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants (in shares)</link:label>
    <link:label id="lab_us-gaap_IncrementalCommonSharesAttributableToCallOptionsAndWarrants_label_en-US" xlink:label="lab_us-gaap_IncrementalCommonSharesAttributableToCallOptionsAndWarrants" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Incremental Common Shares Attributable to Dilutive Effect of Call Options and Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncrementalCommonSharesAttributableToCallOptionsAndWarrants" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncrementalCommonSharesAttributableToCallOptionsAndWarrants"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_019c1404-2530-7e21-9c8e-a753e0b1cf05_periodStartLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Nonvested as of January 1, 2025 (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_019c1404-3f39-77c1-a724-f6afc2fb3e25_periodEndLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Nonvested as of December 31, 2025 (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommitmentsAndContingenciesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions_019c139b-2737-7d04-9f5e-2922c3d9a6e8_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total unrecognized compensation cost</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Nonvested Award, Option, Cost Not yet Recognized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:to="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_019c0d23-93a6-71cb-b3fd-354d2af3c7c6_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by (used in) operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_019c0d6e-79da-79c2-84fc-d3612ea18c86_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by (used in) operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTerm_019cb55f-918c-7eea-a53b-a2daa3703cfe_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, term</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTerm_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTerm" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTerm" xlink:to="lab_us-gaap_DebtInstrumentTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseChangeInFairValueOfTermLoanAmount_019c0e8b-a755-7fe3-9ead-e5bcf5ea65f0_terseLabel_en-US" xlink:label="lab_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseChangeInFairValueOfTermLoanAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of term loan</link:label>
    <link:label id="lab_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseChangeInFairValueOfTermLoanAmount_label_en-US" xlink:label="lab_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseChangeInFairValueOfTermLoanAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Change In Fair Value Of Term Loan, Amount</link:label>
    <link:label id="lab_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseChangeInFairValueOfTermLoanAmount_documentation_en-US" xlink:label="lab_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseChangeInFairValueOfTermLoanAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Change In Fair Value Of Term Loan, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseChangeInFairValueOfTermLoanAmount" xlink:href="blln-20251231.xsd#blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseChangeInFairValueOfTermLoanAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseChangeInFairValueOfTermLoanAmount" xlink:to="lab_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseChangeInFairValueOfTermLoanAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife_019c0e9c-054a-796f-b16e-48a3c5209c76_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property and equipment, useful life</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Useful Life</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentUsefulLife"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock_019c139b-2737-7758-b582-48a3164e7455_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Stock Options Valuation Assumptions</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Share-Based Payment Award, Stock Options, Valuation Assumptions [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote</link:label>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_label_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EquityValuationAssumptionDifferenceFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:to="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoTotalCompAmt_label_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeoTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoTotalCompAmt" xlink:to="lab_ecd_PeoTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_019c1285-31dd-7170-b41c-21ddc4d26b11_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeAxis" xlink:to="lab_us-gaap_LongtermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageExercisePrice_019c139b-2737-7ad3-9eab-28e16fa70138_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vested and expected to vest (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageExercisePrice_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Outstanding, Weighted Average Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageExercisePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageExercisePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageExercisePrice" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageExercisePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MoneyMarketFundsMember_019c0a42-e665-76b1-b4d6-f63b5bcad96d_terseLabel_en-US" xlink:label="lab_us-gaap_MoneyMarketFundsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Money market funds</link:label>
    <link:label id="lab_us-gaap_MoneyMarketFundsMember_label_en-US" xlink:label="lab_us-gaap_MoneyMarketFundsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Money Market Funds [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MoneyMarketFundsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MoneyMarketFundsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MoneyMarketFundsMember" xlink:to="lab_us-gaap_MoneyMarketFundsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodThreeMember_019c12bb-9e5a-7236-a076-9877c78ad349_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodThreeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period Three</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodThreeMember_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodThreeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period Three [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodThreeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPeriodThreeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPeriodThreeMember" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPeriodThreeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansPayableToBank_019c12bb-9e5a-77c5-a241-e318d880b3cd_terseLabel_en-US" xlink:label="lab_us-gaap_LoansPayableToBank" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital advances</link:label>
    <link:label id="lab_us-gaap_LoansPayableToBank_label_en-US" xlink:label="lab_us-gaap_LoansPayableToBank" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Payable to Bank</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansPayableToBank" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansPayableToBank"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansPayableToBank" xlink:to="lab_us-gaap_LoansPayableToBank" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDilutedAbstract_019c124b-3c67-78e4-9f0e-711e237a25b2_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDilutedAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Numerator:</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDilutedAbstract_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDilutedAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Diluted [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersDilutedAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersDilutedAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersDilutedAbstract" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDilutedAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_019c0cdd-5616-78aa-87f0-142070188b53_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityExTransitionPeriod_019c0cb2-8c5f-7922-b6cb-499e1b83768a_terseLabel_en-US" xlink:label="lab_dei_EntityExTransitionPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Ex Transition Period</link:label>
    <link:label id="lab_dei_EntityExTransitionPeriod_label_en-US" xlink:label="lab_dei_EntityExTransitionPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Ex Transition Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityExTransitionPeriod" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityExTransitionPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityExTransitionPeriod" xlink:to="lab_dei_EntityExTransitionPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_019c09f6-68af-7eb5-a586-42cd16af3f44_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Line Items]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConvertibleDebtMember_019c0a63-e3d8-7d6a-9c9b-6b27ff4ed500_terseLabel_en-US" xlink:label="lab_us-gaap_ConvertibleDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Convertible Notes</link:label>
    <link:label id="lab_us-gaap_ConvertibleDebtMember_label_en-US" xlink:label="lab_us-gaap_ConvertibleDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Convertible Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConvertibleDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConvertibleDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConvertibleDebtMember" xlink:to="lab_us-gaap_ConvertibleDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_AuditInformationAbstract_label_en-US" xlink:label="lab_blln_AuditInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Audit Information [Abstract]</link:label>
    <link:label id="lab_blln_AuditInformationAbstract_documentation_en-US" xlink:label="lab_blln_AuditInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Audit Information</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_AuditInformationAbstract" xlink:href="blln-20251231.xsd#blln_AuditInformationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_AuditInformationAbstract" xlink:to="lab_blln_AuditInformationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonRule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:to="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_019c128c-ce25-7052-b457-fbb876c73b2d_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of reportable segments</link:label>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Reportable Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfReportableSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfReportableSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfReportableSegments" xlink:to="lab_us-gaap_NumberOfReportableSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComponentsOfDeferredTaxAssetsAbstract_019c0e7c-6fbd-765a-901c-00b7e1a2978d_terseLabel_en-US" xlink:label="lab_us-gaap_ComponentsOfDeferredTaxAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax assets:</link:label>
    <link:label id="lab_us-gaap_ComponentsOfDeferredTaxAssetsAbstract_label_en-US" xlink:label="lab_us-gaap_ComponentsOfDeferredTaxAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Components of Deferred Tax Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComponentsOfDeferredTaxAssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComponentsOfDeferredTaxAssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComponentsOfDeferredTaxAssetsAbstract" xlink:to="lab_us-gaap_ComponentsOfDeferredTaxAssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdvertisingCostsPolicyTextBlock_019c0e40-110d-7b51-8a84-6b10561db67d_terseLabel_en-US" xlink:label="lab_us-gaap_AdvertisingCostsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Advertising Costs</link:label>
    <link:label id="lab_us-gaap_AdvertisingCostsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_AdvertisingCostsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Advertising Cost [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdvertisingCostsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdvertisingCostsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdvertisingCostsPolicyTextBlock" xlink:to="lab_us-gaap_AdvertisingCostsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_019c0cb2-8c5f-7b44-a3d4-26430bc5f390_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressStateOrProvince"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressStateOrProvince" xlink:to="lab_dei_EntityAddressStateOrProvince" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeasePrincipalPayments_019c0d23-93a7-7cd5-8509-8ebc2ad6edb4_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Principal payments on finance lease liabilities</link:label>
    <link:label id="lab_us-gaap_FinanceLeasePrincipalPayments_label_en-US" xlink:label="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Principal Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeasePrincipalPayments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeasePrincipalPayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeasePrincipalPayments" xlink:to="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:to="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_019c0c7d-352a-7cad-8388-cd827550e24e_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total current liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesCurrent" xlink:to="lab_us-gaap_LiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_IndividualAxis_terseLabel_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individual:</link:label>
    <link:label id="lab_ecd_IndividualAxis_label_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Individual [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_IndividualAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_IndividualAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_IndividualAxis" xlink:to="lab_ecd_IndividualAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedContributionPlanCostRecognized_019c0d40-cb8e-7617-b33b-bea3bb39df66_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanCostRecognized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amount contributed to plan</link:label>
    <link:label id="lab_us-gaap_DefinedContributionPlanCostRecognized_label_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanCostRecognized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Contribution Plan, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedContributionPlanCostRecognized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedContributionPlanCostRecognized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedContributionPlanCostRecognized" xlink:to="lab_us-gaap_DefinedContributionPlanCostRecognized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityDomain_019c0e8f-e36a-77d2-88d1-9cc99ee0c6fc_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction [Domain]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityDomain_label_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxAuthorityDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxAuthorityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxAuthorityDomain" xlink:to="lab_us-gaap_IncomeTaxAuthorityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_019c65c4-eaa0-7d00-b05a-2b118375cef2_terseLabel_en-US" xlink:label="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Right-of-use assets obtained in exchange for new finance lease liabilities</link:label>
    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_label_en-US" xlink:label="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Right-of-Use Asset Obtained in Exchange for Finance Lease Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:to="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentAnnualReport_019c0cb3-dbd0-7fc9-9b19-cf95114b706c_terseLabel_en-US" xlink:label="lab_dei_DocumentAnnualReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Annual Report</link:label>
    <link:label id="lab_dei_DocumentAnnualReport_label_en-US" xlink:label="lab_dei_DocumentAnnualReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Annual Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentAnnualReport" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentAnnualReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentAnnualReport" xlink:to="lab_dei_DocumentAnnualReport" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ResearchAndDevelopmentExpenseMember_019c139b-2738-7459-9d8d-ce5048473844_terseLabel_en-US" xlink:label="lab_us-gaap_ResearchAndDevelopmentExpenseMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Research and development</link:label>
    <link:label id="lab_us-gaap_ResearchAndDevelopmentExpenseMember_label_en-US" xlink:label="lab_us-gaap_ResearchAndDevelopmentExpenseMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Research and Development Expense [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ResearchAndDevelopmentExpenseMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ResearchAndDevelopmentExpenseMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ResearchAndDevelopmentExpenseMember" xlink:to="lab_us-gaap_ResearchAndDevelopmentExpenseMember" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_PaymentsOfLoanTerminationFees_019c12bb-9e5a-740f-9056-3d15f16c2e0f_terseLabel_en-US" xlink:label="lab_blln_PaymentsOfLoanTerminationFees" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payments of loan termination fees</link:label>
    <link:label id="lab_blln_PaymentsOfLoanTerminationFees_label_en-US" xlink:label="lab_blln_PaymentsOfLoanTerminationFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Loan Termination Fees</link:label>
    <link:label id="lab_blln_PaymentsOfLoanTerminationFees_documentation_en-US" xlink:label="lab_blln_PaymentsOfLoanTerminationFees" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments of Loan Termination Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_PaymentsOfLoanTerminationFees" xlink:href="blln-20251231.xsd#blln_PaymentsOfLoanTerminationFees"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_PaymentsOfLoanTerminationFees" xlink:to="lab_blln_PaymentsOfLoanTerminationFees" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_FairValueAdjustmentOfConvertibleNotes_019c0c8b-30ae-7574-bbe6-33f7afdfbb55_terseLabel_en-US" xlink:label="lab_blln_FairValueAdjustmentOfConvertibleNotes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of convertible notes</link:label>
    <link:label id="lab_blln_FairValueAdjustmentOfConvertibleNotes_019c0d23-93a6-7ff7-862f-656b6bb6ed82_negatedTerseLabel_en-US" xlink:label="lab_blln_FairValueAdjustmentOfConvertibleNotes" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of convertible notes</link:label>
    <link:label id="lab_blln_FairValueAdjustmentOfConvertibleNotes_label_en-US" xlink:label="lab_blln_FairValueAdjustmentOfConvertibleNotes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Adjustment Of Convertible Notes</link:label>
    <link:label id="lab_blln_FairValueAdjustmentOfConvertibleNotes_documentation_en-US" xlink:label="lab_blln_FairValueAdjustmentOfConvertibleNotes" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value Adjustment Of Convertible Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_FairValueAdjustmentOfConvertibleNotes" xlink:href="blln-20251231.xsd#blln_FairValueAdjustmentOfConvertibleNotes"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_FairValueAdjustmentOfConvertibleNotes" xlink:to="lab_blln_FairValueAdjustmentOfConvertibleNotes" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_DebtInstrumentRevenueParticipationAgreementPrincipalAmountOfNotes_019c12bb-9e5a-7eb8-bdcc-0ad1f96ae93d_terseLabel_en-US" xlink:label="lab_blln_DebtInstrumentRevenueParticipationAgreementPrincipalAmountOfNotes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue participation agreement, principal amount of notes</link:label>
    <link:label id="lab_blln_DebtInstrumentRevenueParticipationAgreementPrincipalAmountOfNotes_label_en-US" xlink:label="lab_blln_DebtInstrumentRevenueParticipationAgreementPrincipalAmountOfNotes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Revenue Participation Agreement, Principal Amount Of Notes</link:label>
    <link:label id="lab_blln_DebtInstrumentRevenueParticipationAgreementPrincipalAmountOfNotes_documentation_en-US" xlink:label="lab_blln_DebtInstrumentRevenueParticipationAgreementPrincipalAmountOfNotes" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Revenue Participation Agreement, Principal Amount Of Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_DebtInstrumentRevenueParticipationAgreementPrincipalAmountOfNotes" xlink:href="blln-20251231.xsd#blln_DebtInstrumentRevenueParticipationAgreementPrincipalAmountOfNotes"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_DebtInstrumentRevenueParticipationAgreementPrincipalAmountOfNotes" xlink:to="lab_blln_DebtInstrumentRevenueParticipationAgreementPrincipalAmountOfNotes" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:to="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfLongTermDebt_019c668f-c952-7a3b-b03c-c6cbecca8bfb_terseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repayments of long-term debt</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfLongTermDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfLongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RepaymentsOfLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfLongTermDebt" xlink:to="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_019c0cb2-8c5f-7539-82c3-9bb89856b4cd_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_label_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInteractiveDataCurrent" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityInteractiveDataCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerPolicyTextBlock_019c128d-843d-7525-9cf3-dfdf97a3c4d6_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueFromContractWithCustomerPolicyTextBlock"/>
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    <link:label id="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseShareBasedCompensationCost_019c0e8b-a755-7183-b2e9-632bc6f4f727_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseShareBasedCompensationCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock-based compensation</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseShareBasedCompensationCost_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseShareBasedCompensationCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Share-Based Payment Arrangement, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationNondeductibleExpenseShareBasedCompensationCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationNondeductibleExpenseShareBasedCompensationCost"/>
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    <link:label id="lab_us-gaap_DisaggregationOfRevenueTable_019c128c-ba42-7456-bbb7-c6f9b1b3071a_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Table]</link:label>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTable_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisaggregationOfRevenueTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisaggregationOfRevenueTable" xlink:to="lab_us-gaap_DisaggregationOfRevenueTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_019c0e7c-9f7c-77e4-9e6c-9d16e623273a_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net operating loss carryforwards</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Operating Loss Carryforwards</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsOperatingLossCarryforwards"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:to="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_019c09f6-68af-767b-b26c-ee261773ab83_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_019c664d-a087-7078-936c-885f24edc0d3_verboseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Long-Lived Tangible Asset [Axis]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Tangible Asset [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo_019c08d5-2669-7b88-b66d-7fa302467f7d_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:to="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityLiquidationPreferencePerShare_019c0839-6e17-7733-b7e7-6e7e153bf59e_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityLiquidationPreferencePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liquidation preference (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityLiquidationPreferencePerShare_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityLiquidationPreferencePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Liquidation Preference Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityLiquidationPreferencePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityLiquidationPreferencePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityLiquidationPreferencePerShare" xlink:to="lab_us-gaap_TemporaryEquityLiquidationPreferencePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssetsNoncurrent_019c0c7d-352a-7397-912a-c7ea64f81d3b_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other non-current assets</link:label>
    <link:label id="lab_us-gaap_OtherAssetsNoncurrent_label_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssetsNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsNoncurrent" xlink:to="lab_us-gaap_OtherAssetsNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCentralIndexKey_019c0cb2-8c5f-7a01-9225-b3af69b03207_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCentralIndexKey"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCentralIndexKey" xlink:to="lab_dei_EntityCentralIndexKey" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoName_terseLabel_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:label id="lab_ecd_PeoName_label_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeoName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoName" xlink:to="lab_ecd_PeoName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentConvertibleConversionPrice1_019c1285-31dd-7978-bd63-399b9b22d2d4_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentConvertibleConversionPrice1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, convertible, conversion price (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentConvertibleConversionPrice1_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentConvertibleConversionPrice1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Convertible, Conversion Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentConvertibleConversionPrice1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentConvertibleConversionPrice1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentConvertibleConversionPrice1" xlink:to="lab_us-gaap_DebtInstrumentConvertibleConversionPrice1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConversionOfStockByUniqueDescriptionAxis_019c6591-5ff0-704d-a442-5af753c6c4b5_terseLabel_en-US" xlink:label="lab_us-gaap_ConversionOfStockByUniqueDescriptionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Conversion Description [Axis]</link:label>
    <link:label id="lab_us-gaap_ConversionOfStockByUniqueDescriptionAxis_label_en-US" xlink:label="lab_us-gaap_ConversionOfStockByUniqueDescriptionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Conversion Description [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConversionOfStockByUniqueDescriptionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConversionOfStockByUniqueDescriptionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConversionOfStockByUniqueDescriptionAxis" xlink:to="lab_us-gaap_ConversionOfStockByUniqueDescriptionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year</link:label>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_label_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:to="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_019c12d9-bd58-7ae4-beb7-35faae173bbf_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:to="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromCollectionOfNotesReceivable_019c662b-489c-742c-a333-f3b87ed52ae5_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromCollectionOfNotesReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net proceeds from promissory notes</link:label>
    <link:label id="lab_us-gaap_ProceedsFromCollectionOfNotesReceivable_label_en-US" xlink:label="lab_us-gaap_ProceedsFromCollectionOfNotesReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Collection of Notes Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromCollectionOfNotesReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromCollectionOfNotesReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromCollectionOfNotesReceivable" xlink:to="lab_us-gaap_ProceedsFromCollectionOfNotesReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingAggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OutstandingAggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingAggtErrCompAmt" xlink:to="lab_ecd_OutstandingAggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_019c0e79-dec0-7a8f-8151-400ec462da23_periodStartLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Fair value, beginning balance</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_019c0e79-ca25-73fc-8660-a641461f2c21_periodEndLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Fair value, ending balance</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationAwardTrancheOneMember_019c139b-2737-7309-b7b5-37c17bfc2d57_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationAwardTrancheOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Tranche One</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationAwardTrancheOneMember_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationAwardTrancheOneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Tranche One [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationAwardTrancheOneMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationAwardTrancheOneMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationAwardTrancheOneMember" xlink:to="lab_us-gaap_ShareBasedCompensationAwardTrancheOneMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityCurrent_019c0c7d-352a-7884-b124-1bdbf1a69592_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred revenue, current</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityCurrent_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractWithCustomerLiabilityCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:to="lab_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseAbstract_019c7790-ab1b-7470-b168-045f0a486040_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nontaxable or nondeductible items</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Amount [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationNondeductibleExpenseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationNondeductibleExpenseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxReconciliationNondeductibleExpenseAbstract" xlink:to="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_AccruedLegalExpensesCurrent_019c07e1-bb71-7092-a952-471ce395741e_terseLabel_en-US" xlink:label="lab_blln_AccruedLegalExpensesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued legal expenses</link:label>
    <link:label id="lab_blln_AccruedLegalExpensesCurrent_label_en-US" xlink:label="lab_blln_AccruedLegalExpensesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Legal Expenses, Current</link:label>
    <link:label id="lab_blln_AccruedLegalExpensesCurrent_documentation_en-US" xlink:label="lab_blln_AccruedLegalExpensesCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accrued Legal Expenses, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_AccruedLegalExpensesCurrent" xlink:href="blln-20251231.xsd#blln_AccruedLegalExpensesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_AccruedLegalExpensesCurrent" xlink:to="lab_blln_AccruedLegalExpensesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_019c12bb-9e5a-78b3-bf50-d529cee0c2b6_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrant exercise price (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Exercise Price of Warrants or Rights</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:to="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:type="arc" order="1"/>
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    <link:label id="lab_dei_EntityFilerCategory_label_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
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    <link:label id="lab_us-gaap_ClassOfStockDomain_019c0811-1015-7de5-b4f5-4d4f128ac02e_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockDomain" xlink:to="lab_us-gaap_ClassOfStockDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions_019c1e02-46e7-700b-9093-a4514e2a0b3c_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecognized compensation cost</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate"/>
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    <link:label id="lab_us-gaap_ClassOfWarrantOrRightDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Domain]</link:label>
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    <link:label id="lab_us-gaap_VestingDomain_019c139b-2737-7289-9560-183d850bf571_terseLabel_en-US" xlink:label="lab_us-gaap_VestingDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting [Domain]</link:label>
    <link:label id="lab_us-gaap_VestingDomain_label_en-US" xlink:label="lab_us-gaap_VestingDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vesting [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VestingDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VestingDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VestingDomain" xlink:to="lab_us-gaap_VestingDomain" xlink:type="arc" order="1"/>
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    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year [Member]</link:label>
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    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_label_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RepurchaseAgreementCounterpartyNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:to="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_019c08bf-f0fb-712c-bc5a-9d6a4d4cdaaf_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote</link:label>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToPeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToPeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToPeoCompFnTextBlock" xlink:to="lab_ecd_AdjToPeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_019c140c-23a5-7226-a3dd-16a09e85e823_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average remaining contractual life (in years)</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Remaining Contractual Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2" xlink:to="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock_019c07c6-f53c-71b2-812d-e491def10b0d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Accrued Expenses and Other Current Liabilities</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accounts Payable and Accrued Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndTitle_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title</link:label>
    <link:label id="lab_ecd_TrdArrIndTitle_label_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Title</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndTitle" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrIndTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndTitle" xlink:to="lab_ecd_TrdArrIndTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeerGroupTotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:to="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityDisclosureAbstract" xlink:to="lab_us-gaap_TemporaryEquityDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_CommonStockConvertibleNumberOfSharesConvertiblePerShare_019c8fcb-8d0a-7f9d-9e9d-b65c37d700a6_terseLabel_en-US" xlink:label="lab_blln_CommonStockConvertibleNumberOfSharesConvertiblePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion ratio, number of shares convertible per share (in shares)</link:label>
    <link:label id="lab_blln_CommonStockConvertibleNumberOfSharesConvertiblePerShare_label_en-US" xlink:label="lab_blln_CommonStockConvertibleNumberOfSharesConvertiblePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Convertible, Number of Shares Convertible per Share</link:label>
    <link:label id="lab_blln_CommonStockConvertibleNumberOfSharesConvertiblePerShare_documentation_en-US" xlink:label="lab_blln_CommonStockConvertibleNumberOfSharesConvertiblePerShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock, Convertible, Number of Shares Convertible per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_CommonStockConvertibleNumberOfSharesConvertiblePerShare" xlink:href="blln-20251231.xsd#blln_CommonStockConvertibleNumberOfSharesConvertiblePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_CommonStockConvertibleNumberOfSharesConvertiblePerShare" xlink:to="lab_blln_CommonStockConvertibleNumberOfSharesConvertiblePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoMember_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO</link:label>
    <link:label id="lab_ecd_NonPeoNeoMember_label_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonPeoNeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoMember" xlink:to="lab_ecd_NonPeoNeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_019c139b-2737-7e5e-98cc-a740047ba8ca_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate intrinsic value, outstanding</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Intrinsic Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_SeriesB1RedeemableConvertiblePreferredStockMember_019c0887-a6e4-7eb1-9814-aa6d747996d9_terseLabel_en-US" xlink:label="lab_blln_SeriesB1RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series B-1</link:label>
    <link:label id="lab_blln_SeriesB1RedeemableConvertiblePreferredStockMember_label_en-US" xlink:label="lab_blln_SeriesB1RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series B-1 Redeemable Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_blln_SeriesB1RedeemableConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_blln_SeriesB1RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series B-1 Redeemable Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_SeriesB1RedeemableConvertiblePreferredStockMember" xlink:href="blln-20251231.xsd#blln_SeriesB1RedeemableConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_SeriesB1RedeemableConvertiblePreferredStockMember" xlink:to="lab_blln_SeriesB1RedeemableConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_OberlandCapitalMember_019c12bb-9e5a-7af1-8314-58a5c8b73210_terseLabel_en-US" xlink:label="lab_blln_OberlandCapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Oberland Capital</link:label>
    <link:label id="lab_blln_OberlandCapitalMember_label_en-US" xlink:label="lab_blln_OberlandCapitalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Oberland Capital [Member]</link:label>
    <link:label id="lab_blln_OberlandCapitalMember_documentation_en-US" xlink:label="lab_blln_OberlandCapitalMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Oberland Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_OberlandCapitalMember" xlink:href="blln-20251231.xsd#blln_OberlandCapitalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_OberlandCapitalMember" xlink:to="lab_blln_OberlandCapitalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_019c12b4-622c-7fca-ad70-8d16a86580e3_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_label_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsidiarySaleOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:to="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019c12f1-bcbb-7a1c-93d8-e18db21b9ab7_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Award Types</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDebtExtinguishmentCosts_019c0d23-93a7-74c1-a120-9a113ee110ce_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDebtExtinguishmentCosts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payment of exit fee and prepayment payable upon debt extinguishment</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDebtExtinguishmentCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDebtExtinguishmentCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment for Debt Extinguishment or Debt Prepayment Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDebtExtinguishmentCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfDebtExtinguishmentCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDebtExtinguishmentCosts" xlink:to="lab_us-gaap_PaymentsOfDebtExtinguishmentCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_019c08bf-801a-733a-958f-1cf5f008f897_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EqtyAwrdsAdjsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsMember" xlink:to="lab_ecd_EqtyAwrdsAdjsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseholdImprovementsMember_019c09f6-68af-75b4-9252-9a5d3a95cf87_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseholdImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leasehold improvements</link:label>
    <link:label id="lab_us-gaap_LeaseholdImprovementsMember_label_en-US" xlink:label="lab_us-gaap_LeaseholdImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leasehold Improvements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseholdImprovementsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeaseholdImprovementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseholdImprovementsMember" xlink:to="lab_us-gaap_LeaseholdImprovementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdvertisingExpense_019c12c8-f016-7f4e-bef1-c7261f6e11b5_terseLabel_en-US" xlink:label="lab_us-gaap_AdvertisingExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Advertising expense</link:label>
    <link:label id="lab_us-gaap_AdvertisingExpense_label_en-US" xlink:label="lab_us-gaap_AdvertisingExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Advertising Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdvertisingExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdvertisingExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdvertisingExpense" xlink:to="lab_us-gaap_AdvertisingExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PnsnBnftsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:to="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueLineItems_019c128c-ba42-7937-b37f-20d47708ac0a_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Line Items]</link:label>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueLineItems_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisaggregationOfRevenueLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisaggregationOfRevenueLineItems" xlink:to="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OutstandingRecoveryCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryCompAmt" xlink:to="lab_ecd_OutstandingRecoveryCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract_019c0e76-2c67-7686-8bfb-abe87190ad96_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred:</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Expense (Benefit), Continuing Operations [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:to="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_019c1285-31dd-759b-a986-368c2934044c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentNameDomain" xlink:to="lab_us-gaap_DebtInstrumentNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate_019c139b-2737-76c6-9836-91085061644d_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividend yield</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Dividend Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RecoveryOfErrCompDisclosureLineItems_label_en-US" xlink:label="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recovery of Erroneously Awarded Compensation Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RecoveryOfErrCompDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:to="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized_019c128c-ce25-7a6e-b651-e0c34dc966c4_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred revenue recognized</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Liability, Revenue Recognized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractWithCustomerLiabilityRevenueRecognized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:to="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInEmployeeRelatedLiabilities_019c0d23-93a6-7042-b87d-1a656b91ee17_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInEmployeeRelatedLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued compensation and employee benefits</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInEmployeeRelatedLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInEmployeeRelatedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Employee Related Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInEmployeeRelatedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInEmployeeRelatedLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInEmployeeRelatedLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInEmployeeRelatedLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_terseLabel_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value</link:label>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_label_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_MnpiDiscTimedForCompValFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:to="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential_019cada7-f2e8-758c-a26c-5cc00ac315f3_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign tax effects</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Foreign Income Tax Rate Differential, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingDilutedDisclosureItemsAbstract_019c124b-3c67-76b7-b001-707b563d6c7d_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingDilutedDisclosureItemsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Denominator:</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingDilutedDisclosureItemsAbstract_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingDilutedDisclosureItemsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding Reconciliation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingDilutedDisclosureItemsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingDilutedDisclosureItemsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingDilutedDisclosureItemsAbstract" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingDilutedDisclosureItemsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockMember_019c6614-864a-7383-a61c-f6c75a236c89_verboseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Employee stock</link:label>
    <link:label id="lab_us-gaap_EmployeeStockMember_019c660e-e3ee-7910-bb2d-e9d5e386832c_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares available for future issuance under the Employee Stock Purchase Plan</link:label>
    <link:label id="lab_us-gaap_EmployeeStockMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Employee Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockMember" xlink:to="lab_us-gaap_EmployeeStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentsIncorporatedByReferenceTextBlock_019c0cc6-77b5-7405-871b-7c31c80cb98f_terseLabel_en-US" xlink:label="lab_dei_DocumentsIncorporatedByReferenceTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Documents Incorporated by Reference</link:label>
    <link:label id="lab_dei_DocumentsIncorporatedByReferenceTextBlock_label_en-US" xlink:label="lab_dei_DocumentsIncorporatedByReferenceTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Documents Incorporated by Reference [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentsIncorporatedByReferenceTextBlock" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentsIncorporatedByReferenceTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentsIncorporatedByReferenceTextBlock" xlink:to="lab_dei_DocumentsIncorporatedByReferenceTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_SaleOfStockLossOnSale_019c139b-2737-77ea-bad4-6c400a26eb45_terseLabel_en-US" xlink:label="lab_blln_SaleOfStockLossOnSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock-based compensation expense related to the sale of stock</link:label>
    <link:label id="lab_blln_SaleOfStockLossOnSale_label_en-US" xlink:label="lab_blln_SaleOfStockLossOnSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Loss on Sale</link:label>
    <link:label id="lab_blln_SaleOfStockLossOnSale_documentation_en-US" xlink:label="lab_blln_SaleOfStockLossOnSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sale of Stock, Loss on Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_SaleOfStockLossOnSale" xlink:href="blln-20251231.xsd#blln_SaleOfStockLossOnSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_SaleOfStockLossOnSale" xlink:to="lab_blln_SaleOfStockLossOnSale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_019cc0d1-d6eb-7c75-a894-36b6817912f5_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated other comprehensive loss</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_AccruedPhlebotomyExpensesCurrent_019c07e5-1e87-7ed2-921b-47754776dcb5_terseLabel_en-US" xlink:label="lab_blln_AccruedPhlebotomyExpensesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued phlebotomy expenses</link:label>
    <link:label id="lab_blln_AccruedPhlebotomyExpensesCurrent_label_en-US" xlink:label="lab_blln_AccruedPhlebotomyExpensesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Phlebotomy Expenses, Current</link:label>
    <link:label id="lab_blln_AccruedPhlebotomyExpensesCurrent_documentation_en-US" xlink:label="lab_blln_AccruedPhlebotomyExpensesCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accrued Phlebotomy Expenses, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_AccruedPhlebotomyExpensesCurrent" xlink:href="blln-20251231.xsd#blln_AccruedPhlebotomyExpensesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_AccruedPhlebotomyExpensesCurrent" xlink:to="lab_blln_AccruedPhlebotomyExpensesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_WarrantsAndRightsOutstandingGrantDateFairValue_019ca03c-5f02-7725-a53a-b21b3785d79f_terseLabel_en-US" xlink:label="lab_blln_WarrantsAndRightsOutstandingGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total grant date fair value</link:label>
    <link:label id="lab_blln_WarrantsAndRightsOutstandingGrantDateFairValue_label_en-US" xlink:label="lab_blln_WarrantsAndRightsOutstandingGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrants and Rights Outstanding, Grant Date Fair Value</link:label>
    <link:label id="lab_blln_WarrantsAndRightsOutstandingGrantDateFairValue_documentation_en-US" xlink:label="lab_blln_WarrantsAndRightsOutstandingGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Warrants and Rights Outstanding, Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_WarrantsAndRightsOutstandingGrantDateFairValue" xlink:href="blln-20251231.xsd#blln_WarrantsAndRightsOutstandingGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_WarrantsAndRightsOutstandingGrantDateFairValue" xlink:to="lab_blln_WarrantsAndRightsOutstandingGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilities_019c0e81-7b48-78ae-9576-da0c6651d18a_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Total deferred tax liabilities</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilities_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxLiabilities" xlink:to="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainOnExtinguishment_019c1e8d-c71d-7ade-b78f-4f936f2d14c1_negatedTerseLabel_en-US" xlink:label="lab_blln_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainOnExtinguishment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Gain on extinguishment</link:label>
    <link:label id="lab_blln_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainOnExtinguishment_label_en-US" xlink:label="lab_blln_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainOnExtinguishment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Gain on Extinguishment</link:label>
    <link:label id="lab_blln_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainOnExtinguishment_documentation_en-US" xlink:label="lab_blln_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainOnExtinguishment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Gain on Extinguishment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainOnExtinguishment" xlink:href="blln-20251231.xsd#blln_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainOnExtinguishment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainOnExtinguishment" xlink:to="lab_blln_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainOnExtinguishment" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_MeasurementInputInterestRateMember_019c0a63-e3d8-7db4-bac7-dfd9f2af674e_terseLabel_en-US" xlink:label="lab_blln_MeasurementInputInterestRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate</link:label>
    <link:label id="lab_blln_MeasurementInputInterestRateMember_label_en-US" xlink:label="lab_blln_MeasurementInputInterestRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Interest Rate [Member]</link:label>
    <link:label id="lab_blln_MeasurementInputInterestRateMember_documentation_en-US" xlink:label="lab_blln_MeasurementInputInterestRateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_MeasurementInputInterestRateMember" xlink:href="blln-20251231.xsd#blln_MeasurementInputInterestRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_MeasurementInputInterestRateMember" xlink:to="lab_blln_MeasurementInputInterestRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AggtPnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:to="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseOther_019c0e8b-a755-7746-af57-fd2a5f42ec1f_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseOther_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Other, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationNondeductibleExpenseOther" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationNondeductibleExpenseOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxReconciliationNondeductibleExpenseOther" xlink:to="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseOther" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryNet_019c0c7d-352a-7018-ba87-f233c4024fb0_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Inventories</link:label>
    <link:label id="lab_us-gaap_InventoryNet_label_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InventoryNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryNet" xlink:to="lab_us-gaap_InventoryNet" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MinimumMember_019c0885-b09f-733d-820f-9b57610de8a8_terseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum</link:label>
    <link:label id="lab_srt_MinimumMember_label_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Minimum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MinimumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MinimumMember" xlink:to="lab_srt_MinimumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_Q22026Member_019c12bb-9e5a-755a-bd2a-5acaaf730a2c_terseLabel_en-US" xlink:label="lab_blln_Q22026Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Q2 2026</link:label>
    <link:label id="lab_blln_Q22026Member_label_en-US" xlink:label="lab_blln_Q22026Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Q2 2026 [Member]</link:label>
    <link:label id="lab_blln_Q22026Member_documentation_en-US" xlink:label="lab_blln_Q22026Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Q2 2026</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_Q22026Member" xlink:href="blln-20251231.xsd#blln_Q22026Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_Q22026Member" xlink:to="lab_blln_Q22026Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecurityDeposit_019c095b-2225-7313-b23c-ebfeae4d4399_terseLabel_en-US" xlink:label="lab_us-gaap_SecurityDeposit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security deposit</link:label>
    <link:label id="lab_us-gaap_SecurityDeposit_label_en-US" xlink:label="lab_us-gaap_SecurityDeposit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Deposit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecurityDeposit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecurityDeposit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecurityDeposit" xlink:to="lab_us-gaap_SecurityDeposit" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureName_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureName_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CoSelectedMeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureName" xlink:to="lab_ecd_CoSelectedMeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_AntidilutiveSecuritiesWarrantsToPurchaseRedeemableConvertiblePreferredStockMember_019c124b-3c67-73f0-9bb4-f71b16d2a8a7_terseLabel_en-US" xlink:label="lab_blln_AntidilutiveSecuritiesWarrantsToPurchaseRedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants to purchase redeemable convertible preferred stock</link:label>
    <link:label id="lab_blln_AntidilutiveSecuritiesWarrantsToPurchaseRedeemableConvertiblePreferredStockMember_label_en-US" xlink:label="lab_blln_AntidilutiveSecuritiesWarrantsToPurchaseRedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Warrants To Purchase Redeemable Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_blln_AntidilutiveSecuritiesWarrantsToPurchaseRedeemableConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_blln_AntidilutiveSecuritiesWarrantsToPurchaseRedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Warrants To Purchase Redeemable Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_AntidilutiveSecuritiesWarrantsToPurchaseRedeemableConvertiblePreferredStockMember" xlink:href="blln-20251231.xsd#blln_AntidilutiveSecuritiesWarrantsToPurchaseRedeemableConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_AntidilutiveSecuritiesWarrantsToPurchaseRedeemableConvertiblePreferredStockMember" xlink:to="lab_blln_AntidilutiveSecuritiesWarrantsToPurchaseRedeemableConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CostOfSalesPolicyTextBlock_019c0e3f-b672-72d9-912a-5da2b775e64f_terseLabel_en-US" xlink:label="lab_us-gaap_CostOfSalesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cost of Revenue</link:label>
    <link:label id="lab_us-gaap_CostOfSalesPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_CostOfSalesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cost of Goods and Service [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostOfSalesPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CostOfSalesPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CostOfSalesPolicyTextBlock" xlink:to="lab_us-gaap_CostOfSalesPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_terseLabel_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Available</link:label>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_label_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Securities Aggregate Available Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrSecuritiesAggAvailAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:to="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableCurrent_019c0c7d-352a-7360-a061-2f8c4d309e72_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable</link:label>
    <link:label id="lab_us-gaap_AccountsPayableCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsPayableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableCurrent" xlink:to="lab_us-gaap_AccountsPayableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeasePayments_019c08b7-b6f0-70d7-8301-d33870685fcb_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeasePayments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash paid for amounts included in the measurement of operating lease liabilities within operating cash flows</link:label>
    <link:label id="lab_us-gaap_OperatingLeasePayments_label_en-US" xlink:label="lab_us-gaap_OperatingLeasePayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeasePayments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeasePayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeasePayments" xlink:to="lab_us-gaap_OperatingLeasePayments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_terseLabel_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs)</link:label>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_label_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockAppreciationRightsSARSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:to="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_019c0c8b-30ae-7bdc-a52f-071c2cd63c64_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) attributable to common stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_019c124b-3c67-7d44-b539-d6f0bde38615_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) attributable to common stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_019c08a7-63cf-7e01-8e7e-361a37794f18_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommitmentsAndContingenciesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationAwardTrancheTwoMember_019c139b-2737-73cd-a251-8a29c1864f8a_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationAwardTrancheTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Tranche Two</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationAwardTrancheTwoMember_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationAwardTrancheTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Tranche Two [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationAwardTrancheTwoMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationAwardTrancheTwoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationAwardTrancheTwoMember" xlink:to="lab_us-gaap_ShareBasedCompensationAwardTrancheTwoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_ClinicalTrialSupportAndOtherServicesMember_019c128c-ba42-7939-bf9a-f0819c5ed0e2_terseLabel_en-US" xlink:label="lab_blln_ClinicalTrialSupportAndOtherServicesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Clinical trial support and other services</link:label>
    <link:label id="lab_blln_ClinicalTrialSupportAndOtherServicesMember_label_en-US" xlink:label="lab_blln_ClinicalTrialSupportAndOtherServicesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Clinical Trial Support and Other Services [Member]</link:label>
    <link:label id="lab_blln_ClinicalTrialSupportAndOtherServicesMember_documentation_en-US" xlink:label="lab_blln_ClinicalTrialSupportAndOtherServicesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Clinical Trial Support and Other Services</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_ClinicalTrialSupportAndOtherServicesMember" xlink:href="blln-20251231.xsd#blln_ClinicalTrialSupportAndOtherServicesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_ClinicalTrialSupportAndOtherServicesMember" xlink:to="lab_blln_ClinicalTrialSupportAndOtherServicesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019c0c8b-30ae-73fc-b84d-bfbe8f3faa1b_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average shares used in calculating net income (loss) per share, diluted (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019c124b-3c67-71c7-809b-c87862abbeb2_totalLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Weighted-average shares used in calculating net income (loss) per share, diluted (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock_019c0e47-42c1-7ad1-adda-9b7451500a0c_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Information</link:label>
    <link:label id="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:to="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedInPeriodFairValue1_019c6605-c4a4-7143-825b-fbe93e97ac3a_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedInPeriodFairValue1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value vested</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedInPeriodFairValue1_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedInPeriodFairValue1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested in Period, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedInPeriodFairValue1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedInPeriodFairValue1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedInPeriodFairValue1" xlink:to="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedInPeriodFairValue1" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description</link:label>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_label_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonGaapMeasureDescriptionTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:to="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_SeriesDRedeemableConvertiblePreferredStockMember_019c083d-3fdd-78f0-9d81-45a0f5a54902_terseLabel_en-US" xlink:label="lab_blln_SeriesDRedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series D</link:label>
    <link:label id="lab_blln_SeriesDRedeemableConvertiblePreferredStockMember_label_en-US" xlink:label="lab_blln_SeriesDRedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series D Redeemable Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_blln_SeriesDRedeemableConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_blln_SeriesDRedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series D Redeemable Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_SeriesDRedeemableConvertiblePreferredStockMember" xlink:href="blln-20251231.xsd#blln_SeriesDRedeemableConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_SeriesDRedeemableConvertiblePreferredStockMember" xlink:to="lab_blln_SeriesDRedeemableConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitySmallBusiness_019c0cb2-8c5f-75a9-a778-4847ef6e2df1_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:label id="lab_dei_EntitySmallBusiness_label_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitySmallBusiness" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntitySmallBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitySmallBusiness" xlink:to="lab_dei_EntitySmallBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfStockIssuanceCosts_019c0cdd-5616-7b6d-b4d0-2ca17ed2c9de_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfStockIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance costs</link:label>
    <link:label id="lab_us-gaap_PaymentsOfStockIssuanceCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsOfStockIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Stock Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfStockIssuanceCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfStockIssuanceCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfStockIssuanceCosts" xlink:to="lab_us-gaap_PaymentsOfStockIssuanceCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_Q12025Member_019c12bb-9e5a-7109-942e-8458bbd44e32_terseLabel_en-US" xlink:label="lab_blln_Q12025Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Q1 2025</link:label>
    <link:label id="lab_blln_Q12025Member_label_en-US" xlink:label="lab_blln_Q12025Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Q1 2025 [Member]</link:label>
    <link:label id="lab_blln_Q12025Member_documentation_en-US" xlink:label="lab_blln_Q12025Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Q1 2025</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_Q12025Member" xlink:href="blln-20251231.xsd#blln_Q12025Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_Q12025Member" xlink:to="lab_blln_Q12025Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:to="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense_019c65c4-19a7-7257-a067-26ecb6e250a2_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest and penalties associated with unrecognized tax benefits</link:label>
    <link:label id="lab_us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense_label_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecognized Tax Benefits, Income Tax Penalties and Interest Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense" xlink:to="lab_us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CurrentStateAndLocalTaxExpenseBenefit_019c0e76-2c67-791b-afb1-48bffb3afe90_terseLabel_en-US" xlink:label="lab_us-gaap_CurrentStateAndLocalTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">State</link:label>
    <link:label id="lab_us-gaap_CurrentStateAndLocalTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_CurrentStateAndLocalTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current State and Local Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CurrentStateAndLocalTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CurrentStateAndLocalTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CurrentStateAndLocalTaxExpenseBenefit" xlink:to="lab_us-gaap_CurrentStateAndLocalTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtTextBlock_019c1285-31dd-7dab-8eb6-e921fcb3b0f5_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Convertible Notes</link:label>
    <link:label id="lab_us-gaap_LongTermDebtTextBlock_019c12bb-9e5a-7b0e-9681-4dcfbcc0bddf_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt</link:label>
    <link:label id="lab_us-gaap_LongTermDebtTextBlock_label_en-US" xlink:label="lab_us-gaap_LongTermDebtTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtTextBlock" xlink:to="lab_us-gaap_LongTermDebtTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentTransitionReport_019c0cb2-8c5f-7193-8c1b-801e752fb1a0_terseLabel_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:label id="lab_dei_DocumentTransitionReport_label_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentTransitionReport" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentTransitionReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentTransitionReport" xlink:to="lab_dei_DocumentTransitionReport" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_A2021LSACommonStockWarrantsMember_019c12bb-9e5a-775a-9898-dc74033d9c12_terseLabel_en-US" xlink:label="lab_blln_A2021LSACommonStockWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2021 LSA</link:label>
    <link:label id="lab_blln_A2021LSACommonStockWarrantsMember_label_en-US" xlink:label="lab_blln_A2021LSACommonStockWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2021 LSA Common Stock Warrants [Member]</link:label>
    <link:label id="lab_blln_A2021LSACommonStockWarrantsMember_documentation_en-US" xlink:label="lab_blln_A2021LSACommonStockWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2021 LSA Common Stock Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_A2021LSACommonStockWarrantsMember" xlink:href="blln-20251231.xsd#blln_A2021LSACommonStockWarrantsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_A2021LSACommonStockWarrantsMember" xlink:to="lab_blln_A2021LSACommonStockWarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDue_019c08d7-4c1c-717c-afa1-1ce358a0bc64_totalLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total lease payments</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDue_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:to="lab_us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_terseLabel_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Securities</link:label>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_label_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Underlying Securities Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardUndrlygSecuritiesAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:to="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_DeferredTaxLiabilitiesRightOfUseAssets_019c0e80-d2c2-7136-bbc1-fe1143bd1f3a_negatedTerseLabel_en-US" xlink:label="lab_blln_DeferredTaxLiabilitiesRightOfUseAssets" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Right of use asset</link:label>
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    <link:label id="lab_blln_DeferredTaxLiabilitiesRightOfUseAssets_documentation_en-US" xlink:label="lab_blln_DeferredTaxLiabilitiesRightOfUseAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Right of Use Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_DeferredTaxLiabilitiesRightOfUseAssets" xlink:href="blln-20251231.xsd#blln_DeferredTaxLiabilitiesRightOfUseAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_DeferredTaxLiabilitiesRightOfUseAssets" xlink:to="lab_blln_DeferredTaxLiabilitiesRightOfUseAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityComponentDomain_019c0cdd-5616-79c2-8932-48820687a3e7_terseLabel_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:label id="lab_us-gaap_EquityComponentDomain_label_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityComponentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityComponentDomain" xlink:to="lab_us-gaap_EquityComponentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentPeriodEndDate_019c0cb2-8c5f-7a05-afbd-cac59409e89a_terseLabel_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:label id="lab_dei_DocumentPeriodEndDate_label_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentPeriodEndDate"/>
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    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember_019c0a42-e665-7e59-bc3c-5110e49e0691_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents [Domain]</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember_label_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember" xlink:to="lab_us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_019c0e71-b65e-7523-877f-910b403b0778_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:to="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivable_019c12ba-0aa9-78f1-9a93-6181afe75ac4_terseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for credit losses</link:label>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivable_label_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:to="lab_us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonClassAMember_019c0c82-11c8-78c3-b88d-8a34d4ab7eb7_terseLabel_en-US" xlink:label="lab_us-gaap_CommonClassAMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Class A</link:label>
    <link:label id="lab_us-gaap_CommonClassAMember_label_en-US" xlink:label="lab_us-gaap_CommonClassAMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Class A [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassAMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonClassAMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonClassAMember" xlink:to="lab_us-gaap_CommonClassAMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Table</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardsCloseToMnpiDiscTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShortTermLeaseCost_019c0968-2b12-7a2c-8ad2-c701fda468b1_terseLabel_en-US" xlink:label="lab_us-gaap_ShortTermLeaseCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Short-term lease costs</link:label>
    <link:label id="lab_us-gaap_ShortTermLeaseCost_label_en-US" xlink:label="lab_us-gaap_ShortTermLeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermLeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortTermLeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortTermLeaseCost" xlink:to="lab_us-gaap_ShortTermLeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableWeightedAverageRemainingContractualTerm1_019c140c-23a5-79a7-ad78-26e77f9133f3_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableWeightedAverageRemainingContractualTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average remaining contractual life, vested and exercisable (in years)</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableWeightedAverageRemainingContractualTerm1_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableWeightedAverageRemainingContractualTerm1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercisable, Weighted Average Remaining Contractual Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableWeightedAverageRemainingContractualTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableWeightedAverageRemainingContractualTerm1"/>
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    <link:label id="lab_blln_TemporaryEquityDissolutionAsPartOfReorganizationMinimumPercentage_019c089c-429f-77a7-95c2-561639209ece_terseLabel_en-US" xlink:label="lab_blln_TemporaryEquityDissolutionAsPartOfReorganizationMinimumPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Temporary equity, redemption percentage</link:label>
    <link:label id="lab_blln_TemporaryEquityDissolutionAsPartOfReorganizationMinimumPercentage_label_en-US" xlink:label="lab_blln_TemporaryEquityDissolutionAsPartOfReorganizationMinimumPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Dissolution as Part of Reorganization, Minimum Percentage</link:label>
    <link:label id="lab_blln_TemporaryEquityDissolutionAsPartOfReorganizationMinimumPercentage_documentation_en-US" xlink:label="lab_blln_TemporaryEquityDissolutionAsPartOfReorganizationMinimumPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Dissolution as Part of Reorganization, Minimum Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_TemporaryEquityDissolutionAsPartOfReorganizationMinimumPercentage" xlink:href="blln-20251231.xsd#blln_TemporaryEquityDissolutionAsPartOfReorganizationMinimumPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_TemporaryEquityDissolutionAsPartOfReorganizationMinimumPercentage" xlink:to="lab_blln_TemporaryEquityDissolutionAsPartOfReorganizationMinimumPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability_019c0d23-93a6-7c89-965f-89fbecf194d6_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Operating Lease Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOperatingLeaseLiability"/>
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    <link:label id="lab_us-gaap_TreasuryStockAcquiredAverageCostPerShare_label_en-US" xlink:label="lab_us-gaap_TreasuryStockAcquiredAverageCostPerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Acquired, Average Cost Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockAcquiredAverageCostPerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TreasuryStockAcquiredAverageCostPerShare"/>
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    <link:label id="lab_us-gaap_AdditionalPaidInCapital_019c0c7d-352a-7b74-9f1d-31c1e89bda8b_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional paid-in capital</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalPaidInCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapital" xlink:to="lab_us-gaap_AdditionalPaidInCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductOrServiceAxis_019c128c-ba42-7065-be03-9356a3b55f15_terseLabel_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:label id="lab_srt_ProductOrServiceAxis_label_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductOrServiceAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProductOrServiceAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductOrServiceAxis" xlink:to="lab_srt_ProductOrServiceAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableLeaseCost_019c0963-8989-700e-999a-af8f60dfbbeb_terseLabel_en-US" xlink:label="lab_us-gaap_VariableLeaseCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable lease expense</link:label>
    <link:label id="lab_us-gaap_VariableLeaseCost_label_en-US" xlink:label="lab_us-gaap_VariableLeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableLeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableLeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableLeaseCost" xlink:to="lab_us-gaap_VariableLeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_019c0c8b-30ae-7746-a868-32b90c5c93dc_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer, Excluding Assessed Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber_019c139b-2737-7f57-ae46-6f7d2a4b048f_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vested and expected to vest (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Outstanding, Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsCurrent_019c0c7d-352a-71f0-9028-663e1683bb92_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total current assets</link:label>
    <link:label id="lab_us-gaap_AssetsCurrent_label_en-US" xlink:label="lab_us-gaap_AssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsCurrent" xlink:to="lab_us-gaap_AssetsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_019c0885-8e98-78c5-9beb-f13a3606945b_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriodWeightedAverageExercisePrice_019c139b-2737-7a26-b742-29626f4567ce_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriodWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forfeited or expired (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriodWeightedAverageExercisePrice_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriodWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Forfeitures and Expirations in Period, Weighted Average Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriodWeightedAverageExercisePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriodWeightedAverageExercisePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriodWeightedAverageExercisePrice" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriodWeightedAverageExercisePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_LesseeOperatingLeaseNumberOfRenewalOptions_019c1e9a-b947-747a-ba0d-4e0658e3640d_terseLabel_en-US" xlink:label="lab_blln_LesseeOperatingLeaseNumberOfRenewalOptions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of extend options</link:label>
    <link:label id="lab_blln_LesseeOperatingLeaseNumberOfRenewalOptions_label_en-US" xlink:label="lab_blln_LesseeOperatingLeaseNumberOfRenewalOptions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Number of Renewal Options</link:label>
    <link:label id="lab_blln_LesseeOperatingLeaseNumberOfRenewalOptions_documentation_en-US" xlink:label="lab_blln_LesseeOperatingLeaseNumberOfRenewalOptions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Number of Renewal Options</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_LesseeOperatingLeaseNumberOfRenewalOptions" xlink:href="blln-20251231.xsd#blln_LesseeOperatingLeaseNumberOfRenewalOptions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_LesseeOperatingLeaseNumberOfRenewalOptions" xlink:to="lab_blln_LesseeOperatingLeaseNumberOfRenewalOptions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems_019c0a54-7f44-7cc5-aa7c-5ea4131dd180_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_AggtErrCompAmt_label_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompAmt" xlink:to="lab_ecd_AggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_SeriesA2RedeemableConvertiblePreferredStockMember_019c0887-a6e4-7fc5-981c-8c0bbd988e54_terseLabel_en-US" xlink:label="lab_blln_SeriesA2RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series A-2</link:label>
    <link:label id="lab_blln_SeriesA2RedeemableConvertiblePreferredStockMember_label_en-US" xlink:label="lab_blln_SeriesA2RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series A-2 Redeemable Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_blln_SeriesA2RedeemableConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_blln_SeriesA2RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series A-2 Redeemable Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_SeriesA2RedeemableConvertiblePreferredStockMember" xlink:href="blln-20251231.xsd#blln_SeriesA2RedeemableConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_SeriesA2RedeemableConvertiblePreferredStockMember" xlink:to="lab_blln_SeriesA2RedeemableConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue_019c1e02-46e7-743d-a158-a1a462892385_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intrinsic values of options exercised</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercises in Period, Intrinsic Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodTotalIntrinsicValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareDilutedLineItems_019c124b-3c67-7943-88e9-42a9545bc18a_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDilutedLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDilutedLineItems_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDilutedLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDilutedLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareDilutedLineItems"/>
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    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote</link:label>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_label_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeerGroupIssuersFnTextBlock"/>
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    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_019c0c8b-30ae-79b3-9708-2e08773f54f9_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) attributable to common stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_019cc481-2ad9-7681-8d12-b48d035408ae_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive loss, net of taxes</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_019cc0e2-f3ce-7869-b683-663853c3d481_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive loss</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent"/>
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    <link:label id="lab_us-gaap_LiabilitiesCurrentAbstract_019c0c7d-352a-715f-93c2-49af0b966139_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current liabilities:</link:label>
    <link:label id="lab_us-gaap_LiabilitiesCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Current [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesCurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesCurrentAbstract" xlink:to="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_OperatingExpenses_label_en-US" xlink:label="lab_us-gaap_OperatingExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses</link:label>
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    <link:label id="lab_blln_ExerciseOfStockOptionsForWhichCashHasNotBeenReceived_label_en-US" xlink:label="lab_blln_ExerciseOfStockOptionsForWhichCashHasNotBeenReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Exercise Of Stock Options For Which Cash Has not Been Received</link:label>
    <link:label id="lab_blln_ExerciseOfStockOptionsForWhichCashHasNotBeenReceived_documentation_en-US" xlink:label="lab_blln_ExerciseOfStockOptionsForWhichCashHasNotBeenReceived" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Exercise Of Stock Options For Which Cash Has not Been Received</link:label>
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    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel1Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel1Member"/>
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    <link:label id="lab_us-gaap_GainLossOnDispositionOfAssets1_label_en-US" xlink:label="lab_us-gaap_GainLossOnDispositionOfAssets1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Disposition of Assets</link:label>
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    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsLineItems_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Expensed and Capitalized, Amount [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsLineItems"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInAccruedLiabilities"/>
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    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_019c124f-2694-7815-90c7-293788183e08_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable"/>
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    <link:label id="lab_us-gaap_EarningsPerShareDiluted_019c0c8b-30ae-7c0c-a206-2d5d1afe7f69_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) per share, diluted (in dollars per share)</link:label>
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    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_019c0c7d-352a-797f-8afe-7fac526e8625_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, after Allowance for Credit Loss, Current</link:label>
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    <link:label id="lab_blln_CommonStockWarrantsMember_documentation_en-US" xlink:label="lab_blln_CommonStockWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock Warrants</link:label>
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    <link:label id="lab_dei_AuditorLocation_label_en-US" xlink:label="lab_dei_AuditorLocation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Auditor Location</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AuditorLocation" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AuditorLocation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AuditorLocation" xlink:to="lab_dei_AuditorLocation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GrossProfit_019c0c8b-30ae-7bcc-abd0-1faace6c5204_totalLabel_en-US" xlink:label="lab_us-gaap_GrossProfit" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Gross profit</link:label>
    <link:label id="lab_us-gaap_GrossProfit_label_en-US" xlink:label="lab_us-gaap_GrossProfit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gross Profit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GrossProfit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GrossProfit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GrossProfit" xlink:to="lab_us-gaap_GrossProfit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue_019c0cdd-5616-7742-9e29-85782d59a0ba_negatedLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Repurchase of common stock</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased and Retired During Period, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockRepurchasedAndRetiredDuringPeriodValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue" xlink:to="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_Q42025Member_019c12bb-9e5a-7da5-a0ac-c412abcf6775_terseLabel_en-US" xlink:label="lab_blln_Q42025Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Q4 2025</link:label>
    <link:label id="lab_blln_Q42025Member_label_en-US" xlink:label="lab_blln_Q42025Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Q4 2025 [Member]</link:label>
    <link:label id="lab_blln_Q42025Member_documentation_en-US" xlink:label="lab_blln_Q42025Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Q4 2025</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_Q42025Member" xlink:href="blln-20251231.xsd#blln_Q42025Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_Q42025Member" xlink:to="lab_blln_Q42025Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DomesticCountryMember_019c0e8f-e36a-7489-9dab-1e999b314eb6_terseLabel_en-US" xlink:label="lab_us-gaap_DomesticCountryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Domestic Tax Jurisdiction</link:label>
    <link:label id="lab_us-gaap_DomesticCountryMember_label_en-US" xlink:label="lab_us-gaap_DomesticCountryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Domestic Tax Jurisdiction [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DomesticCountryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DomesticCountryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DomesticCountryMember" xlink:to="lab_us-gaap_DomesticCountryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_019c08cd-7360-759e-971c-421a7376e6ae_negatedLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Less: imputed interest</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, Undiscounted Excess Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_LoansPayableToBankFinalPayment_019c668f-c952-7ed5-985c-3726eac926d6_terseLabel_en-US" xlink:label="lab_blln_LoansPayableToBankFinalPayment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans payable to bank, final payment</link:label>
    <link:label id="lab_blln_LoansPayableToBankFinalPayment_label_en-US" xlink:label="lab_blln_LoansPayableToBankFinalPayment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Payable to Bank, Final Payment</link:label>
    <link:label id="lab_blln_LoansPayableToBankFinalPayment_documentation_en-US" xlink:label="lab_blln_LoansPayableToBankFinalPayment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loans Payable to Bank, Final Payment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_LoansPayableToBankFinalPayment" xlink:href="blln-20251231.xsd#blln_LoansPayableToBankFinalPayment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_LoansPayableToBankFinalPayment" xlink:to="lab_blln_LoansPayableToBankFinalPayment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOther_019c65cc-3e8d-76ce-99c6-2e6e0c90dd04_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOther_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Other, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOther" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOther" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOther" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_019c0d23-93a7-702d-ab04-d88de474d978_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash paid for income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_019c4d50-0e85-7ca1-bb82-ec3f498b8fe8_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total taxes paid</link:label>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_label_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Taxes Paid, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxesPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxesPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxesPaidNet" xlink:to="lab_us-gaap_IncomeTaxesPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquitySharesIssued_019c0c7d-352a-768b-8664-e0fbbea6b40a_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redeemable convertible preferred stock, issued (in shares)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesIssued_019c0811-1015-735a-b547-f99aae13938b_verboseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesIssued" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Shares Issued (in shares)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesIssued_label_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Shares Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquitySharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquitySharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquitySharesIssued" xlink:to="lab_us-gaap_TemporaryEquitySharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_019c6679-27a4-73ca-a00f-cb02d53ac215_totalLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Long-term debt, net</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentCarryingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:to="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_019c139b-2737-7c3f-9447-772293fccada_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Granted (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Grants in Period, Weighted Average Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityWellKnownSeasonedIssuer_019c0cb6-a6a2-7ce3-bb0b-7a8ce9fbbcc6_terseLabel_en-US" xlink:label="lab_dei_EntityWellKnownSeasonedIssuer" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Well-known Seasoned Issuer</link:label>
    <link:label id="lab_dei_EntityWellKnownSeasonedIssuer_label_en-US" xlink:label="lab_dei_EntityWellKnownSeasonedIssuer" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Well-known Seasoned Issuer</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityWellKnownSeasonedIssuer" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityWellKnownSeasonedIssuer"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityWellKnownSeasonedIssuer" xlink:to="lab_dei_EntityWellKnownSeasonedIssuer" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_NumberOfExecutives_019c1e02-7edf-7261-b9f6-cc1ae32d4587_terseLabel_en-US" xlink:label="lab_blln_NumberOfExecutives" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of executives</link:label>
    <link:label id="lab_blln_NumberOfExecutives_label_en-US" xlink:label="lab_blln_NumberOfExecutives" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Executives</link:label>
    <link:label id="lab_blln_NumberOfExecutives_documentation_en-US" xlink:label="lab_blln_NumberOfExecutives" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Executives</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_NumberOfExecutives" xlink:href="blln-20251231.xsd#blln_NumberOfExecutives"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_NumberOfExecutives" xlink:to="lab_blln_NumberOfExecutives" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock_019c09f3-866c-7a55-9105-7356f806f33e_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property and Equipment, Net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_019c08cb-c3ed-7c82-ac99-270cb99fd2ff_totalLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total lease payments</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_LoansPayableToBankInterestOnlyPeriod_019c668e-6c99-7be9-a314-d974d565db2b_terseLabel_en-US" xlink:label="lab_blln_LoansPayableToBankInterestOnlyPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest only period</link:label>
    <link:label id="lab_blln_LoansPayableToBankInterestOnlyPeriod_label_en-US" xlink:label="lab_blln_LoansPayableToBankInterestOnlyPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Payable to Bank, Interest Only Period</link:label>
    <link:label id="lab_blln_LoansPayableToBankInterestOnlyPeriod_documentation_en-US" xlink:label="lab_blln_LoansPayableToBankInterestOnlyPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loans Payable to Bank, Interest Only Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_LoansPayableToBankInterestOnlyPeriod" xlink:href="blln-20251231.xsd#blln_LoansPayableToBankInterestOnlyPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_LoansPayableToBankInterestOnlyPeriod" xlink:to="lab_blln_LoansPayableToBankInterestOnlyPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_DebtInstrumentRedemptionPeriodSixMember_019c12bb-9e5a-757b-bd8c-321da3c736a6_terseLabel_en-US" xlink:label="lab_blln_DebtInstrumentRedemptionPeriodSixMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period Six</link:label>
    <link:label id="lab_blln_DebtInstrumentRedemptionPeriodSixMember_label_en-US" xlink:label="lab_blln_DebtInstrumentRedemptionPeriodSixMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period Six [Member]</link:label>
    <link:label id="lab_blln_DebtInstrumentRedemptionPeriodSixMember_documentation_en-US" xlink:label="lab_blln_DebtInstrumentRedemptionPeriodSixMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period Six</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_DebtInstrumentRedemptionPeriodSixMember" xlink:href="blln-20251231.xsd#blln_DebtInstrumentRedemptionPeriodSixMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_DebtInstrumentRedemptionPeriodSixMember" xlink:to="lab_blln_DebtInstrumentRedemptionPeriodSixMember" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseChangeInFairValueOfTermLoanPercent_019c65cb-29d1-7ba5-b87d-81d1b9dc4418_terseLabel_en-US" xlink:label="lab_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseChangeInFairValueOfTermLoanPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of term loan</link:label>
    <link:label id="lab_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseChangeInFairValueOfTermLoanPercent_label_en-US" xlink:label="lab_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseChangeInFairValueOfTermLoanPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Change In Fair Value Of Term Loan, Percent</link:label>
    <link:label id="lab_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseChangeInFairValueOfTermLoanPercent_documentation_en-US" xlink:label="lab_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseChangeInFairValueOfTermLoanPercent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Change In Fair Value Of Term Loan, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseChangeInFairValueOfTermLoanPercent" xlink:href="blln-20251231.xsd#blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseChangeInFairValueOfTermLoanPercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseChangeInFairValueOfTermLoanPercent" xlink:to="lab_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseChangeInFairValueOfTermLoanPercent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrExpirationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expiration Date</link:label>
    <link:label id="lab_ecd_TrdArrExpirationDate_label_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Expiration Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrExpirationDate" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrExpirationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrExpirationDate" xlink:to="lab_ecd_TrdArrExpirationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_ClassOfWarrantOrRightSharesWarrantsIssuedDuringPeriod_019c12bb-9e5a-76da-8762-fa50ff8b4d46_terseLabel_en-US" xlink:label="lab_blln_ClassOfWarrantOrRightSharesWarrantsIssuedDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants issued during period (in shares)</link:label>
    <link:label id="lab_blln_ClassOfWarrantOrRightSharesWarrantsIssuedDuringPeriod_label_en-US" xlink:label="lab_blln_ClassOfWarrantOrRightSharesWarrantsIssuedDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Shares, Warrants Issued During Period</link:label>
    <link:label id="lab_blln_ClassOfWarrantOrRightSharesWarrantsIssuedDuringPeriod_documentation_en-US" xlink:label="lab_blln_ClassOfWarrantOrRightSharesWarrantsIssuedDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Shares, Warrants Issued During Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_ClassOfWarrantOrRightSharesWarrantsIssuedDuringPeriod" xlink:href="blln-20251231.xsd#blln_ClassOfWarrantOrRightSharesWarrantsIssuedDuringPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_ClassOfWarrantOrRightSharesWarrantsIssuedDuringPeriod" xlink:to="lab_blln_ClassOfWarrantOrRightSharesWarrantsIssuedDuringPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_019c0c7d-352a-77bb-b423-b00df936949c_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property and equipment, net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_019c09f6-68af-70aa-8825-5967e01379fc_totalLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Property and equipment, net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentNet" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsNetIncomeTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsReceivable_019c0d23-93a6-75c5-af47-e3e6c8f28d8a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsReceivable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accounts Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInAccountsReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:to="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryPolicyTextBlock_019c0e1b-19c5-7440-94bb-a9f8dd9e85ea_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Inventories</link:label>
    <link:label id="lab_us-gaap_InventoryPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_InventoryPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InventoryPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryPolicyTextBlock" xlink:to="lab_us-gaap_InventoryPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_CostOfProductAndServiceSoldMember_019c139b-2738-7159-a2f0-6e1abca2cdb8_terseLabel_en-US" xlink:label="lab_blln_CostOfProductAndServiceSoldMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cost of revenue</link:label>
    <link:label id="lab_blln_CostOfProductAndServiceSoldMember_label_en-US" xlink:label="lab_blln_CostOfProductAndServiceSoldMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cost of Product And Service Sold [Member]</link:label>
    <link:label id="lab_blln_CostOfProductAndServiceSoldMember_documentation_en-US" xlink:label="lab_blln_CostOfProductAndServiceSoldMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cost of Product And Service Sold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_CostOfProductAndServiceSoldMember" xlink:href="blln-20251231.xsd#blln_CostOfProductAndServiceSoldMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_CostOfProductAndServiceSoldMember" xlink:to="lab_blln_CostOfProductAndServiceSoldMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCurrentReportingStatus_019c0cb2-8c5f-7aca-9690-2c78bbb9a03c_terseLabel_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:label id="lab_dei_EntityCurrentReportingStatus_label_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCurrentReportingStatus" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCurrentReportingStatus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCurrentReportingStatus" xlink:to="lab_dei_EntityCurrentReportingStatus" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_AdjustmentsToAdditionalPaidInCapitalRepaymentsOfPromissoryNoteReceivable_019c657c-58e0-751d-8727-42f42337344b_terseLabel_en-US" xlink:label="lab_blln_AdjustmentsToAdditionalPaidInCapitalRepaymentsOfPromissoryNoteReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repayment of promissory notes by executives</link:label>
    <link:label id="lab_blln_AdjustmentsToAdditionalPaidInCapitalRepaymentsOfPromissoryNoteReceivable_label_en-US" xlink:label="lab_blln_AdjustmentsToAdditionalPaidInCapitalRepaymentsOfPromissoryNoteReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustments to Additional Paid in Capital, Repayments of Promissory Note Receivable</link:label>
    <link:label id="lab_blln_AdjustmentsToAdditionalPaidInCapitalRepaymentsOfPromissoryNoteReceivable_documentation_en-US" xlink:label="lab_blln_AdjustmentsToAdditionalPaidInCapitalRepaymentsOfPromissoryNoteReceivable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Adjustments to Additional Paid in Capital, Repayments of Promissory Note Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_AdjustmentsToAdditionalPaidInCapitalRepaymentsOfPromissoryNoteReceivable" xlink:href="blln-20251231.xsd#blln_AdjustmentsToAdditionalPaidInCapitalRepaymentsOfPromissoryNoteReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_AdjustmentsToAdditionalPaidInCapitalRepaymentsOfPromissoryNoteReceivable" xlink:to="lab_blln_AdjustmentsToAdditionalPaidInCapitalRepaymentsOfPromissoryNoteReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardsCloseToMnpiDiscTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate_019c0e8b-a755-798b-a354-565c6f19c877_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tax at the federal statutory rate</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation at Federal Statutory Income Tax Rate, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" xlink:to="lab_us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_019c0c84-fd99-7aff-96de-a0c43c0662e3_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfFinancialPositionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:to="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_terseLabel_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Executive Category:</link:label>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_label_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Executive Category [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ExecutiveCategoryAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ExecutiveCategoryAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ExecutiveCategoryAxis" xlink:to="lab_ecd_ExecutiveCategoryAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_LoansPayableToBankNumberOfEqualMonthlyPayments_019c1e09-faf6-7124-98bc-185cde8ee5fa_terseLabel_en-US" xlink:label="lab_blln_LoansPayableToBankNumberOfEqualMonthlyPayments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of equal monthly payments</link:label>
    <link:label id="lab_blln_LoansPayableToBankNumberOfEqualMonthlyPayments_label_en-US" xlink:label="lab_blln_LoansPayableToBankNumberOfEqualMonthlyPayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Payable to Bank, Number of Equal Monthly Payments</link:label>
    <link:label id="lab_blln_LoansPayableToBankNumberOfEqualMonthlyPayments_documentation_en-US" xlink:label="lab_blln_LoansPayableToBankNumberOfEqualMonthlyPayments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loans Payable to Bank, Number of Equal Monthly Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_LoansPayableToBankNumberOfEqualMonthlyPayments" xlink:href="blln-20251231.xsd#blln_LoansPayableToBankNumberOfEqualMonthlyPayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_LoansPayableToBankNumberOfEqualMonthlyPayments" xlink:to="lab_blln_LoansPayableToBankNumberOfEqualMonthlyPayments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseShareBasedCompensationCost_019c65c9-73fb-7bb8-9593-7335c65fcbe5_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseShareBasedCompensationCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock-based compensation</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseShareBasedCompensationCost_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseShareBasedCompensationCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Share-Based Payment Arrangement, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseShareBasedCompensationCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseShareBasedCompensationCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseShareBasedCompensationCost" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseShareBasedCompensationCost" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_SettlementOfCommonStockWarrantLiability_019c0d66-66e6-710f-9f52-8ba6f65bff22_terseLabel_en-US" xlink:label="lab_blln_SettlementOfCommonStockWarrantLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Settlement of common stock warrant liability</link:label>
    <link:label id="lab_blln_SettlementOfCommonStockWarrantLiability_label_en-US" xlink:label="lab_blln_SettlementOfCommonStockWarrantLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Settlement Of Common Stock Warrant Liability</link:label>
    <link:label id="lab_blln_SettlementOfCommonStockWarrantLiability_documentation_en-US" xlink:label="lab_blln_SettlementOfCommonStockWarrantLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Settlement Of Common Stock Warrant Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_SettlementOfCommonStockWarrantLiability" xlink:href="blln-20251231.xsd#blln_SettlementOfCommonStockWarrantLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_SettlementOfCommonStockWarrantLiability" xlink:to="lab_blln_SettlementOfCommonStockWarrantLiability" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_RepaymentsOfDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Debt</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeasesTextBlock_019c08af-8a60-75cf-8496-4fe8d51bdad7_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeasesTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Leases [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeasesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeasesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeasesTextBlock" xlink:to="lab_us-gaap_LesseeOperatingLeasesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_019c0d23-93a7-74ee-abe1-418f8be27fb7_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by financing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureAxis_terseLabel_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measure:</link:label>
    <link:label id="lab_ecd_MeasureAxis_label_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_MeasureAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureAxis" xlink:to="lab_ecd_MeasureAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_FairValueAdjustmentOfRedeemableConvertiblePreferredStockWarrantLiability_019c0d23-93a6-75b0-9e7d-454496952d5c_negatedTerseLabel_en-US" xlink:label="lab_blln_FairValueAdjustmentOfRedeemableConvertiblePreferredStockWarrantLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of redeemable convertible preferred stock warrant liability</link:label>
    <link:label id="lab_blln_FairValueAdjustmentOfRedeemableConvertiblePreferredStockWarrantLiability_label_en-US" xlink:label="lab_blln_FairValueAdjustmentOfRedeemableConvertiblePreferredStockWarrantLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Adjustment Of Redeemable Convertible Preferred Stock Warrant Liability</link:label>
    <link:label id="lab_blln_FairValueAdjustmentOfRedeemableConvertiblePreferredStockWarrantLiability_documentation_en-US" xlink:label="lab_blln_FairValueAdjustmentOfRedeemableConvertiblePreferredStockWarrantLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value Adjustment Of Redeemable Convertible Preferred Stock Warrant Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_FairValueAdjustmentOfRedeemableConvertiblePreferredStockWarrantLiability" xlink:href="blln-20251231.xsd#blln_FairValueAdjustmentOfRedeemableConvertiblePreferredStockWarrantLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_FairValueAdjustmentOfRedeemableConvertiblePreferredStockWarrantLiability" xlink:to="lab_blln_FairValueAdjustmentOfRedeemableConvertiblePreferredStockWarrantLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_AdjustmentToAdditionalPaidInCapitalVestingOfEarlyExercises_019c0cdd-5616-7598-b1f4-b164f9f37777_terseLabel_en-US" xlink:label="lab_blln_AdjustmentToAdditionalPaidInCapitalVestingOfEarlyExercises" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting of early exercises</link:label>
    <link:label id="lab_blln_AdjustmentToAdditionalPaidInCapitalVestingOfEarlyExercises_label_en-US" xlink:label="lab_blln_AdjustmentToAdditionalPaidInCapitalVestingOfEarlyExercises" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment To Additional Paid In Capital, Vesting Of Early Exercises</link:label>
    <link:label id="lab_blln_AdjustmentToAdditionalPaidInCapitalVestingOfEarlyExercises_documentation_en-US" xlink:label="lab_blln_AdjustmentToAdditionalPaidInCapitalVestingOfEarlyExercises" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Adjustment To Additional Paid In Capital, Vesting Of Early Exercises</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_AdjustmentToAdditionalPaidInCapitalVestingOfEarlyExercises" xlink:href="blln-20251231.xsd#blln_AdjustmentToAdditionalPaidInCapitalVestingOfEarlyExercises"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_AdjustmentToAdditionalPaidInCapitalVestingOfEarlyExercises" xlink:to="lab_blln_AdjustmentToAdditionalPaidInCapitalVestingOfEarlyExercises" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_Q32026Member_019c12bb-9e5a-7859-96b4-0089692adfee_terseLabel_en-US" xlink:label="lab_blln_Q32026Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Q3 2026</link:label>
    <link:label id="lab_blln_Q32026Member_label_en-US" xlink:label="lab_blln_Q32026Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Q3 2026 [Member]</link:label>
    <link:label id="lab_blln_Q32026Member_documentation_en-US" xlink:label="lab_blln_Q32026Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Q3 2026</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_Q32026Member" xlink:href="blln-20251231.xsd#blln_Q32026Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_Q32026Member" xlink:to="lab_blln_Q32026Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForLoans_019c12bb-9e5a-76cf-965e-ab26344a16a6_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForLoans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepayment of outstanding term loan</link:label>
    <link:label id="lab_us-gaap_PaymentsForLoans_label_en-US" xlink:label="lab_us-gaap_PaymentsForLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForLoans" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForLoans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForLoans" xlink:to="lab_us-gaap_PaymentsForLoans" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_CommonStockConvertibleNonActiveBoardMemberTerm_019c8ff6-8bf9-73f9-98ba-bc72c2796ac0_terseLabel_en-US" xlink:label="lab_blln_CommonStockConvertibleNonActiveBoardMemberTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, convertible, non-active board member term</link:label>
    <link:label id="lab_blln_CommonStockConvertibleNonActiveBoardMemberTerm_label_en-US" xlink:label="lab_blln_CommonStockConvertibleNonActiveBoardMemberTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Convertible, Non-Active Board Member Term</link:label>
    <link:label id="lab_blln_CommonStockConvertibleNonActiveBoardMemberTerm_documentation_en-US" xlink:label="lab_blln_CommonStockConvertibleNonActiveBoardMemberTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock, Convertible, Non-Active Board Member Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_CommonStockConvertibleNonActiveBoardMemberTerm" xlink:href="blln-20251231.xsd#blln_CommonStockConvertibleNonActiveBoardMemberTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_CommonStockConvertibleNonActiveBoardMemberTerm" xlink:to="lab_blln_CommonStockConvertibleNonActiveBoardMemberTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_019c09f6-68af-7193-b27a-401b779ea7e3_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_019c664d-c2e9-7961-ba6d-0e1ca1405ce5_verboseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Long-Lived Tangible Asset [Domain]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Tangible Asset [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CostOfGoodsAndServicesSold_019c0c8b-30ae-78da-9a32-d147271f94b5_terseLabel_en-US" xlink:label="lab_us-gaap_CostOfGoodsAndServicesSold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cost of revenue</link:label>
    <link:label id="lab_us-gaap_CostOfGoodsAndServicesSold_label_en-US" xlink:label="lab_us-gaap_CostOfGoodsAndServicesSold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cost of Product and Service Sold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostOfGoodsAndServicesSold" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CostOfGoodsAndServicesSold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CostOfGoodsAndServicesSold" xlink:to="lab_us-gaap_CostOfGoodsAndServicesSold" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure, Table</link:label>
    <link:label id="lab_ecd_PvpTableTextBlock_label_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PvpTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTableTextBlock" xlink:to="lab_ecd_PvpTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_019c12f7-77e9-7c12-bd07-62cf8511c3eb_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Risk-free interest rate</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Risk Free Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_019c0d23-93a6-746f-9f3a-87c9980ff656_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of debt discount costs and accretion of exit fees</link:label>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_label_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Debt Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfFinancingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AmortizationOfFinancingCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfFinancingCosts" xlink:to="lab_us-gaap_AmortizationOfFinancingCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_019c0cb2-8c5f-70aa-8da5-91d1d5a5f3a2_terseLabel_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_label_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityTaxIdentificationNumber" xlink:to="lab_dei_EntityTaxIdentificationNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_Q22025Member_019c12bb-9e5a-7a09-8639-bd33365ba702_terseLabel_en-US" xlink:label="lab_blln_Q22025Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Q2 2025</link:label>
    <link:label id="lab_blln_Q22025Member_label_en-US" xlink:label="lab_blln_Q22025Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Q2 2025 [Member]</link:label>
    <link:label id="lab_blln_Q22025Member_documentation_en-US" xlink:label="lab_blln_Q22025Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Q2 2025</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_Q22025Member" xlink:href="blln-20251231.xsd#blln_Q22025Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_Q22025Member" xlink:to="lab_blln_Q22025Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_019c139b-2737-7086-990f-894b697f28d8_periodStartLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_019c139b-2737-732b-86c5-023e68ac8cce_periodEndLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_019c0c7d-352a-78a2-9fbf-8f1ebafa6128_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, issued (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesIssued" xlink:to="lab_us-gaap_CommonStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_Q42026Member_019c12bb-9e5a-73cc-a1c9-36adb366a90a_terseLabel_en-US" xlink:label="lab_blln_Q42026Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Q4 2026</link:label>
    <link:label id="lab_blln_Q42026Member_label_en-US" xlink:label="lab_blln_Q42026Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Q4 2026 [Member]</link:label>
    <link:label id="lab_blln_Q42026Member_documentation_en-US" xlink:label="lab_blln_Q42026Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Q4 2026</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_Q42026Member" xlink:href="blln-20251231.xsd#blln_Q42026Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_Q42026Member" xlink:to="lab_blln_Q42026Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_019c096c-7311-7703-94d0-2ea3680545b0_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, weighted average remaining lease term</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Weighted Average Remaining Lease Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:to="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_FairValueAdjustmentOfTermLoan_019c0d23-93a6-7e94-b368-1879b72a575b_negatedTerseLabel_en-US" xlink:label="lab_blln_FairValueAdjustmentOfTermLoan" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of term loan</link:label>
    <link:label id="lab_blln_FairValueAdjustmentOfTermLoan_label_en-US" xlink:label="lab_blln_FairValueAdjustmentOfTermLoan" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Adjustment Of Term Loan</link:label>
    <link:label id="lab_blln_FairValueAdjustmentOfTermLoan_documentation_en-US" xlink:label="lab_blln_FairValueAdjustmentOfTermLoan" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value Adjustment Of Term Loan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_FairValueAdjustmentOfTermLoan" xlink:href="blln-20251231.xsd#blln_FairValueAdjustmentOfTermLoan"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_FairValueAdjustmentOfTermLoan" xlink:to="lab_blln_FairValueAdjustmentOfTermLoan" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_TemporaryEquityMinimumNumberOfSharesOutstandingDirectorElectionThreshold_019c661e-7639-740f-a5a0-0bbac71e0188_terseLabel_en-US" xlink:label="lab_blln_TemporaryEquityMinimumNumberOfSharesOutstandingDirectorElectionThreshold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Temporary equity, minimum number of shares outstanding, director election threshold (in shares)</link:label>
    <link:label id="lab_blln_TemporaryEquityMinimumNumberOfSharesOutstandingDirectorElectionThreshold_label_en-US" xlink:label="lab_blln_TemporaryEquityMinimumNumberOfSharesOutstandingDirectorElectionThreshold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Minimum Number of Shares Outstanding, Director Election Threshold</link:label>
    <link:label id="lab_blln_TemporaryEquityMinimumNumberOfSharesOutstandingDirectorElectionThreshold_documentation_en-US" xlink:label="lab_blln_TemporaryEquityMinimumNumberOfSharesOutstandingDirectorElectionThreshold" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Minimum Number of Shares Outstanding, Director Election Threshold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_TemporaryEquityMinimumNumberOfSharesOutstandingDirectorElectionThreshold" xlink:href="blln-20251231.xsd#blln_TemporaryEquityMinimumNumberOfSharesOutstandingDirectorElectionThreshold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_TemporaryEquityMinimumNumberOfSharesOutstandingDirectorElectionThreshold" xlink:to="lab_blln_TemporaryEquityMinimumNumberOfSharesOutstandingDirectorElectionThreshold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseNonoperating_019c0c8b-30ae-7ea3-b7ce-64afa1e1c420_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseNonoperating" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseNonoperating_label_en-US" xlink:label="lab_us-gaap_InterestExpenseNonoperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Nonoperating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseNonoperating" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseNonoperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseNonoperating" xlink:to="lab_us-gaap_InterestExpenseNonoperating" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TradingArrAxis_terseLabel_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangement:</link:label>
    <link:label id="lab_ecd_TradingArrAxis_label_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TradingArrAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrAxis" xlink:to="lab_ecd_TradingArrAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnAmt" xlink:to="lab_ecd_TotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings_019c0e75-67bf-7ffa-a4e6-744122068caa_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to fair value</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Gain (Loss) Included in Earnings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentMeasurementInput_019c0a5b-be1a-7d27-af01-1cd888023426_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument measurement input</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentMeasurementInput_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentMeasurementInput" xlink:to="lab_us-gaap_DebtInstrumentMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_SecurityExchangeName_019c0cb2-8c5f-7a2d-a378-95c7875a5732_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:label id="lab_dei_SecurityExchangeName_label_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_SecurityExchangeName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_SecurityExchangeName" xlink:to="lab_dei_SecurityExchangeName" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_CommonStockConvertibleTermDeathOrIncapacitation_019c8ff6-8bf9-70bd-86c8-26d50cef7af8_terseLabel_en-US" xlink:label="lab_blln_CommonStockConvertibleTermDeathOrIncapacitation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, convertible, death or incapacitation term</link:label>
    <link:label id="lab_blln_CommonStockConvertibleTermDeathOrIncapacitation_label_en-US" xlink:label="lab_blln_CommonStockConvertibleTermDeathOrIncapacitation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Convertible, Term, Death or Incapacitation</link:label>
    <link:label id="lab_blln_CommonStockConvertibleTermDeathOrIncapacitation_documentation_en-US" xlink:label="lab_blln_CommonStockConvertibleTermDeathOrIncapacitation" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock, Convertible, Term, Death or Incapacitation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_CommonStockConvertibleTermDeathOrIncapacitation" xlink:href="blln-20251231.xsd#blln_CommonStockConvertibleTermDeathOrIncapacitation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_CommonStockConvertibleTermDeathOrIncapacitation" xlink:to="lab_blln_CommonStockConvertibleTermDeathOrIncapacitation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid_019c0d23-93a7-729a-803d-9b19d59a5b34_terseLabel_en-US" xlink:label="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchases of property and equipment in accounts payable and accrued expenses and other current liabilities</link:label>
    <link:label id="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid_label_en-US" xlink:label="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capital Expenditures Incurred but Not yet Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalExpendituresIncurredButNotYetPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:to="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsPreferredStock_019ca022-c806-77b7-ac69-4f936aca7dda_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsPreferredStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends declared or paid</link:label>
    <link:label id="lab_us-gaap_DividendsPreferredStock_label_en-US" xlink:label="lab_us-gaap_DividendsPreferredStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends, Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsPreferredStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsPreferredStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsPreferredStock" xlink:to="lab_us-gaap_DividendsPreferredStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceInitialPublicOffering_019c0883-4bfe-7b65-8f6e-e8ea7f30695e_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceInitialPublicOffering" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from issuance of Class A common stock in connection with the Company&#8217;s initial public offering, net of underwriting discounts and commissions</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceInitialPublicOffering_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceInitialPublicOffering" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance Initial Public Offering</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceInitialPublicOffering" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromIssuanceInitialPublicOffering"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceInitialPublicOffering" xlink:to="lab_us-gaap_ProceedsFromIssuanceInitialPublicOffering" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodShares_019c139b-2737-71a6-b39e-4c89898813eb_terseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares repurchased (in shares)</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodShares_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased During Period, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedDuringPeriodShares" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockRepurchasedDuringPeriodShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchasedDuringPeriodShares" xlink:to="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_019c0c8b-30ae-758a-b28b-83ecc980def2_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating expenses:</link:label>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpensesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpensesAbstract" xlink:to="lab_us-gaap_OperatingExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLeaseNotYetCommencedRenewalTerm1_019ca02e-e099-750b-b999-44e36755eb43_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLeaseNotYetCommencedRenewalTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Extension term</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLeaseNotYetCommencedRenewalTerm1_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLeaseNotYetCommencedRenewalTerm1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Lease Not yet Commenced, Renewal Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLeaseNotYetCommencedRenewalTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLeaseNotYetCommencedRenewalTerm1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLeaseNotYetCommencedRenewalTerm1" xlink:to="lab_us-gaap_LesseeOperatingLeaseLeaseNotYetCommencedRenewalTerm1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RedeemableConvertiblePreferredStockMember_019c0a49-876a-755d-8b79-a8d6beef7a49_terseLabel_en-US" xlink:label="lab_us-gaap_RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redeemable convertible preferred stock warrants</link:label>
    <link:label id="lab_us-gaap_RedeemableConvertiblePreferredStockMember_label_en-US" xlink:label="lab_us-gaap_RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Redeemable Convertible Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RedeemableConvertiblePreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RedeemableConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RedeemableConvertiblePreferredStockMember" xlink:to="lab_us-gaap_RedeemableConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_EquipmentUnderFinanceLeasesMember_019c6614-c69a-7fa8-86d4-ea3ad99a2041_terseLabel_en-US" xlink:label="lab_blln_EquipmentUnderFinanceLeasesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equipment under finance leases</link:label>
    <link:label id="lab_blln_EquipmentUnderFinanceLeasesMember_label_en-US" xlink:label="lab_blln_EquipmentUnderFinanceLeasesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equipment Under Finance Leases [Member]</link:label>
    <link:label id="lab_blln_EquipmentUnderFinanceLeasesMember_documentation_en-US" xlink:label="lab_blln_EquipmentUnderFinanceLeasesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equipment Under Finance Leases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_EquipmentUnderFinanceLeasesMember" xlink:href="blln-20251231.xsd#blln_EquipmentUnderFinanceLeasesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_EquipmentUnderFinanceLeasesMember" xlink:to="lab_blln_EquipmentUnderFinanceLeasesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward_019c0cdd-5616-7850-b91e-03e24dee624a_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redeemable Convertible Preferred Stock</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Temporary Equity [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInTemporaryEquityRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:to="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_Q32025Member_019c12bb-9e5a-7aa8-ab44-a0b23ba7b198_terseLabel_en-US" xlink:label="lab_blln_Q32025Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Q3 2025</link:label>
    <link:label id="lab_blln_Q32025Member_label_en-US" xlink:label="lab_blln_Q32025Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Q3 2025 [Member]</link:label>
    <link:label id="lab_blln_Q32025Member_documentation_en-US" xlink:label="lab_blln_Q32025Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Q3 2025</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_Q32025Member" xlink:href="blln-20251231.xsd#blln_Q32025Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_Q32025Member" xlink:to="lab_blln_Q32025Member" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseDebtExtinguishmentGainOrLossAmount_019c0e8b-a755-751e-82f1-72fb0f36d11f_terseLabel_en-US" xlink:label="lab_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseDebtExtinguishmentGainOrLossAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt extinguishment gain or loss</link:label>
    <link:label id="lab_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseDebtExtinguishmentGainOrLossAmount_label_en-US" xlink:label="lab_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseDebtExtinguishmentGainOrLossAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Debt Extinguishment Gain or Loss, Amount</link:label>
    <link:label id="lab_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseDebtExtinguishmentGainOrLossAmount_documentation_en-US" xlink:label="lab_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseDebtExtinguishmentGainOrLossAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Debt Extinguishment Gain or Loss, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseDebtExtinguishmentGainOrLossAmount" xlink:href="blln-20251231.xsd#blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseDebtExtinguishmentGainOrLossAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseDebtExtinguishmentGainOrLossAmount" xlink:to="lab_blln_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseDebtExtinguishmentGainOrLossAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementLineItems_019c0c82-11c8-773a-9c33-e35c10461135_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:label id="lab_us-gaap_StatementLineItems_label_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementLineItems" xlink:to="lab_us-gaap_StatementLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_Rule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:to="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_019c0c7d-352a-7cd7-932d-2ac3bfec8657_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable_019c0a54-7f44-7a90-a3f9-75e679b705d9_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockMember_019c0a46-7732-700e-b5d7-853a056ee45b_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_label_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockMember" xlink:to="lab_us-gaap_CommonStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_019c1403-7276-7c27-9225-44a5cb8b872d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Vested (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Vested in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract_019c6653-3a34-7042-b192-7038b2c8e98c_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year ending December 31:</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Fiscal Year Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract" xlink:to="lab_us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockLineItems_019c5851-fc32-74cf-bb23-ac7f41127235_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsidiary, Sale of Stock [Line Items]</link:label>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockLineItems_label_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary, Sale of Stock [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiarySaleOfStockLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsidiarySaleOfStockLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="lab_us-gaap_SubsidiarySaleOfStockLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_019c0d23-93a7-7b50-99b9-c9590d422ff1_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net increase in cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Including Exchange Rate Effect and Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedProfessionalFeesCurrent_019c07c9-2d4a-7a65-894c-2b5744b61167_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedProfessionalFeesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued professional services</link:label>
    <link:label id="lab_us-gaap_AccruedProfessionalFeesCurrent_label_en-US" xlink:label="lab_us-gaap_AccruedProfessionalFeesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Professional Fees, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedProfessionalFeesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccruedProfessionalFeesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedProfessionalFeesCurrent" xlink:to="lab_us-gaap_AccruedProfessionalFeesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_019c09de-36e5-7553-a628-0e2842770c8c_terseLabel_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Significant Accounting Policies</link:label>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_label_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Significant Accounting Policies [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SignificantAccountingPoliciesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeMember_019c0885-8e98-7936-a008-a658f72d9274_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:label id="lab_srt_RangeMember_label_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeMember" xlink:to="lab_srt_RangeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive_019c08c5-d0da-7382-8055-1b75232aa1b9_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, after Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_LoansPayableCapitalAdvancesNumberOfTranches_019c12bb-9e5a-756a-a29a-a3b916005c17_terseLabel_en-US" xlink:label="lab_blln_LoansPayableCapitalAdvancesNumberOfTranches" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital advances, number of tranches</link:label>
    <link:label id="lab_blln_LoansPayableCapitalAdvancesNumberOfTranches_label_en-US" xlink:label="lab_blln_LoansPayableCapitalAdvancesNumberOfTranches" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Payable, Capital Advances, Number of Tranches</link:label>
    <link:label id="lab_blln_LoansPayableCapitalAdvancesNumberOfTranches_documentation_en-US" xlink:label="lab_blln_LoansPayableCapitalAdvancesNumberOfTranches" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loans Payable, Capital Advances, Number of Tranches</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_LoansPayableCapitalAdvancesNumberOfTranches" xlink:href="blln-20251231.xsd#blln_LoansPayableCapitalAdvancesNumberOfTranches"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_LoansPayableCapitalAdvancesNumberOfTranches" xlink:to="lab_blln_LoansPayableCapitalAdvancesNumberOfTranches" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionStartDateAxis_019c1e7a-ee12-76c6-994e-0a57f817efea_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionStartDateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Start Date [Axis]</link:label>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionStartDateAxis_label_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionStartDateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Start Date [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionStartDateAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionStartDateAxis"/>
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    <link:label id="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock_019c0e1e-3442-7975-9be0-3f4f62b27798_terseLabel_en-US" xlink:label="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Impairment of Long-Lived Assets</link:label>
    <link:label id="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impairment or Disposal of Long-Lived Assets, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock" xlink:to="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerPerformanceObligationSatisfiedInPreviousPeriod_019cd7ea-bfce-72bc-949b-2e42b90517ed_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerPerformanceObligationSatisfiedInPreviousPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue related to performance obligations satisfied in prior periods</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerPerformanceObligationSatisfiedInPreviousPeriod_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerPerformanceObligationSatisfiedInPreviousPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Performance Obligation Satisfied in Previous Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerPerformanceObligationSatisfiedInPreviousPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractWithCustomerPerformanceObligationSatisfiedInPreviousPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerPerformanceObligationSatisfiedInPreviousPeriod" xlink:to="lab_us-gaap_ContractWithCustomerPerformanceObligationSatisfiedInPreviousPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeasesAbstract_label_en-US" xlink:label="lab_us-gaap_LeasesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leases [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeasesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeasesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeasesAbstract" xlink:to="lab_us-gaap_LeasesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasicAbstract_019c124b-3c67-7d5e-9ab3-7b49fce0bc5e_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic net income (loss) per share:</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasicAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasicAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareBasicAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasicAbstract" xlink:to="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsPayable_019c0d23-93a6-7269-b26e-81188e4fae1a_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsPayable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accounts Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInAccountsPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccountsPayable" xlink:to="lab_us-gaap_IncreaseDecreaseInAccountsPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TradingArrByIndTable_terseLabel_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual</link:label>
    <link:label id="lab_ecd_TradingArrByIndTable_label_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrByIndTable" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TradingArrByIndTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrByIndTable" xlink:to="lab_ecd_TradingArrByIndTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_019c0c8b-30ae-7d04-9ccf-d5d05a564af9_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) per share, basic (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasic" xlink:to="lab_us-gaap_EarningsPerShareBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract_019c12db-443c-7650-877b-6c43373383e9_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities:</link:label>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Fair Value Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesFairValueDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:to="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_019c139b-2737-7d9b-a83f-a0992773161b_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total common stock reserved (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_label_en-US" xlink:label="lab_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Capital Shares Reserved for Future Issuance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockCapitalSharesReservedForFutureIssuance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:to="lab_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxContingencies_019c65cf-de35-76cc-af17-206b2fc7c4fb_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxContingencies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in unrecognized tax benefit</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxContingencies_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxContingencies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Tax Contingency, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationTaxContingencies" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationTaxContingencies"/>
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    <link:label id="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable_019c5851-ac4d-725f-aed8-8af70c720fb3_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsidiary or Equity Method Investee, Sale of Stock, Type [Table]</link:label>
    <link:label id="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable_label_en-US" xlink:label="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary or Equity Method Investee, Sale of Stock, Type [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable"/>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsGross_019c0e7f-bcbb-739e-8e60-dfc9d37b0657_totalLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsGross" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total deferred tax asset</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsGross_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsGross"/>
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    <link:label id="lab_us-gaap_MeasurementInputDiscountRateMember_019c0a6e-a851-7427-9b3e-097ead69ffb6_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discount rate</link:label>
    <link:label id="lab_us-gaap_MeasurementInputDiscountRateMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Discount Rate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputDiscountRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputDiscountRateMember"/>
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    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodAxis_019c12bb-9e5a-7441-8a91-c80a691eefe0_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period [Axis]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPeriodAxis"/>
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    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligation_019c128c-ce25-745e-b1d9-3aa172f4addb_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remaining performance obligations</link:label>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligation_label_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueRemainingPerformanceObligation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueRemainingPerformanceObligation"/>
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    <link:label id="lab_us-gaap_MeasurementInputTypeDomain_019c0a53-cdd8-7189-9020-db40a1262db6_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Domain]</link:label>
    <link:label id="lab_us-gaap_MeasurementInputTypeDomain_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputTypeDomain" xlink:to="lab_us-gaap_MeasurementInputTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgMnpiDiscTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:to="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ResearchAndDevelopmentExpensePolicy_019c0e40-7543-7314-87a1-19262dbfeb65_terseLabel_en-US" xlink:label="lab_us-gaap_ResearchAndDevelopmentExpensePolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Research and Development</link:label>
    <link:label id="lab_us-gaap_ResearchAndDevelopmentExpensePolicy_label_en-US" xlink:label="lab_us-gaap_ResearchAndDevelopmentExpensePolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Research and Development Expense, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ResearchAndDevelopmentExpensePolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ResearchAndDevelopmentExpensePolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ResearchAndDevelopmentExpensePolicy" xlink:to="lab_us-gaap_ResearchAndDevelopmentExpensePolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_019c139b-2737-7bbb-abae-47cf2713957c_terseLabel_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total stock-based compensation</link:label>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_label_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllocatedShareBasedCompensationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllocatedShareBasedCompensationExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllocatedShareBasedCompensationExpense" xlink:to="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsCurrentAbstract_019c0c7d-352a-776b-98f9-c20367acd02b_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current assets:</link:label>
    <link:label id="lab_us-gaap_AssetsCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Current [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsCurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsCurrentAbstract" xlink:to="lab_us-gaap_AssetsCurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_019c0c7d-352a-7154-be43-069bbe612f1d_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities, redeemable convertible preferred stock, and stockholders&#8217; equity</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_019c124b-3c67-765c-bef7-298c95ccee3c_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward_019c139b-2737-750b-a955-2361d314181d_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of Options Outstanding</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_DeferredOfferingCostsPolicyPolicyTextBlock_019c660c-00f3-7c50-ab17-cc474b7ceff9_terseLabel_en-US" xlink:label="lab_blln_DeferredOfferingCostsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred Offering Costs</link:label>
    <link:label id="lab_blln_DeferredOfferingCostsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_blln_DeferredOfferingCostsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Offering Costs, Policy [Policy Text Block]</link:label>
    <link:label id="lab_blln_DeferredOfferingCostsPolicyPolicyTextBlock_documentation_en-US" xlink:label="lab_blln_DeferredOfferingCostsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Offering Costs, Policy</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_DeferredOfferingCostsPolicyPolicyTextBlock" xlink:href="blln-20251231.xsd#blln_DeferredOfferingCostsPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_DeferredOfferingCostsPolicyPolicyTextBlock" xlink:to="lab_blln_DeferredOfferingCostsPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOther_019c0e7c-9f7c-70b1-bf82-547811831b85_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOther_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Other</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOther" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsOther" xlink:to="lab_us-gaap_DeferredTaxAssetsOther" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_label_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountingPoliciesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountingPoliciesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountingPoliciesAbstract" xlink:to="lab_us-gaap_AccountingPoliciesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_019c08bc-be40-7886-9677-2d91a6ec6c31_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Future Lease Payments Under Operating Leases</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Maturity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseMealsAndEntertainment_019c65c7-6762-76a0-91cc-1fd2ddcb107b_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseMealsAndEntertainment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Meals</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseMealsAndEntertainment_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseMealsAndEntertainment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Meals and Entertainment, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationNondeductibleExpenseMealsAndEntertainment" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationNondeductibleExpenseMealsAndEntertainment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxReconciliationNondeductibleExpenseMealsAndEntertainment" xlink:to="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseMealsAndEntertainment" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PayVsPerformanceDisclosureLineItems_label_en-US" xlink:label="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PayVsPerformanceDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:to="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightAxis_019c0a46-5d42-754e-8bdb-3fd4d6341cb9_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Axis]</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightAxis_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfWarrantOrRightAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightAxis" xlink:to="lab_us-gaap_ClassOfWarrantOrRightAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_DebtCovenantTrancheThreeMember_019c12bb-9e5a-7839-944d-2133738b1309_terseLabel_en-US" xlink:label="lab_blln_DebtCovenantTrancheThreeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Third Tranche</link:label>
    <link:label id="lab_blln_DebtCovenantTrancheThreeMember_label_en-US" xlink:label="lab_blln_DebtCovenantTrancheThreeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Covenant, Tranche Three [Member]</link:label>
    <link:label id="lab_blln_DebtCovenantTrancheThreeMember_documentation_en-US" xlink:label="lab_blln_DebtCovenantTrancheThreeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Covenant, Tranche Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_DebtCovenantTrancheThreeMember" xlink:href="blln-20251231.xsd#blln_DebtCovenantTrancheThreeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_DebtCovenantTrancheThreeMember" xlink:to="lab_blln_DebtCovenantTrancheThreeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_019c08c9-86dd-7060-a656-e7b7bcb0a44b_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Present value of operating lease liabilities</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiability" xlink:to="lab_us-gaap_OperatingLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansPayableFairValueDisclosure_019c0a44-af3e-78f8-86dd-4c43d3c2bbee_terseLabel_en-US" xlink:label="lab_us-gaap_LoansPayableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Term loan</link:label>
    <link:label id="lab_us-gaap_LoansPayableFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LoansPayableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Payable, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansPayableFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansPayableFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansPayableFairValueDisclosure" xlink:to="lab_us-gaap_LoansPayableFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SummaryOfValuationAllowanceTextBlock_019cd085-c1ae-7f9d-9202-6b7e0b48d2d6_terseLabel_en-US" xlink:label="lab_us-gaap_SummaryOfValuationAllowanceTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Valuation Allowance</link:label>
    <link:label id="lab_us-gaap_SummaryOfValuationAllowanceTextBlock_label_en-US" xlink:label="lab_us-gaap_SummaryOfValuationAllowanceTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Summary of Valuation Allowance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SummaryOfValuationAllowanceTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SummaryOfValuationAllowanceTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SummaryOfValuationAllowanceTextBlock" xlink:to="lab_us-gaap_SummaryOfValuationAllowanceTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_ShareBasedPaymentArrangementEarlyExerciseOptionsMember_019c661f-cba4-7c5a-b0ad-7988cfaa4d34_terseLabel_en-US" xlink:label="lab_blln_ShareBasedPaymentArrangementEarlyExerciseOptionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Early Exercise Options</link:label>
    <link:label id="lab_blln_ShareBasedPaymentArrangementEarlyExerciseOptionsMember_label_en-US" xlink:label="lab_blln_ShareBasedPaymentArrangementEarlyExerciseOptionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Early Exercise Options [Member]</link:label>
    <link:label id="lab_blln_ShareBasedPaymentArrangementEarlyExerciseOptionsMember_documentation_en-US" xlink:label="lab_blln_ShareBasedPaymentArrangementEarlyExerciseOptionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Early Exercise Options</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_ShareBasedPaymentArrangementEarlyExerciseOptionsMember" xlink:href="blln-20251231.xsd#blln_ShareBasedPaymentArrangementEarlyExerciseOptionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_ShareBasedPaymentArrangementEarlyExerciseOptionsMember" xlink:to="lab_blln_ShareBasedPaymentArrangementEarlyExerciseOptionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DepreciationAndAmortization_019c0d23-93a6-76f6-b5bf-ec6b5696cf51_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization</link:label>
    <link:label id="lab_us-gaap_DepreciationAndAmortization_label_en-US" xlink:label="lab_us-gaap_DepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation, Depletion and Amortization, Nonproduction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DepreciationAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DepreciationAndAmortization" xlink:to="lab_us-gaap_DepreciationAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAssetAmortization_019c08df-80f3-7b0d-8f24-2c3000141b7c_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAssetAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of right-of-use assets:</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAssetAmortization_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAssetAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Right-of-Use Asset, Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseRightOfUseAssetAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseRightOfUseAssetAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseRightOfUseAssetAmortization" xlink:to="lab_us-gaap_FinanceLeaseRightOfUseAssetAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesNoncurrent_019c0c7d-352a-7230-aa66-6a1cbaf176ce_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other non-current liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesNoncurrent_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLiabilitiesNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesNoncurrent" xlink:to="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_A2024NotesMember_019c12bb-9e5a-7141-8d5c-e26a7c3844a0_terseLabel_en-US" xlink:label="lab_blln_A2024NotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2024 Notes</link:label>
    <link:label id="lab_blln_A2024NotesMember_label_en-US" xlink:label="lab_blln_A2024NotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2024 Notes [Member]</link:label>
    <link:label id="lab_blln_A2024NotesMember_documentation_en-US" xlink:label="lab_blln_A2024NotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2024 Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_A2024NotesMember" xlink:href="blln-20251231.xsd#blln_A2024NotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_A2024NotesMember" xlink:to="lab_blln_A2024NotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain_019c12bb-9e5a-7a92-8db9-734d98220d0a_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPeriodDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherAccountsPayableAndAccruedLiabilities_019c0d23-93a6-7923-b824-36440c45c09c_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherAccountsPayableAndAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses and other current liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherAccountsPayableAndAccruedLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherAccountsPayableAndAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Accounts Payable and Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherAccountsPayableAndAccruedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOtherAccountsPayableAndAccruedLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherAccountsPayableAndAccruedLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherAccountsPayableAndAccruedLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtCurrent_019c1312-219e-7e0d-8f9e-60d627907351_negatedLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtCurrent" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Less: current portion</link:label>
    <link:label id="lab_us-gaap_LongTermDebtCurrent_label_en-US" xlink:label="lab_us-gaap_LongTermDebtCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Current Maturities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtCurrent" xlink:to="lab_us-gaap_LongTermDebtCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightUnissued_019c12bb-9e5a-79be-b5cf-a0f4999c52fb_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightUnissued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants exercisable (in shares)</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightUnissued_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightUnissued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Unissued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightUnissued" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfWarrantOrRightUnissued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightUnissued" xlink:to="lab_us-gaap_ClassOfWarrantOrRightUnissued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:to="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CoSelectedMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureAmt" xlink:to="lab_ecd_CoSelectedMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_019c08c2-b85b-7b36-9113-13eb97b0de77_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_019c0c8b-30ae-759e-9c3d-6d4b91f98537_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Comprehensive income (loss), net of taxes</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomeNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_019c0a53-cdd8-7397-b11f-0cae126bdcc6_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputTypeAxis" xlink:to="lab_us-gaap_MeasurementInputTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureName_terseLabel_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_MeasureName_label_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_MeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureName" xlink:to="lab_ecd_MeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock_019c0e71-e564-7e72-8d56-d2b6be2efeff_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Provision for Income Taxes</link:label>
    <link:label id="lab_us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Income before Income Tax, Domestic and Foreign [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_019c0a0b-59bf-7619-a8dd-54b6d0ee190d_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Changes in the Fair Value Instruments</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_019c139b-2737-7be6-b654-59a42c62d787_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_label_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfStockLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockLineItems" xlink:to="lab_us-gaap_ClassOfStockLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebt_019c0c7d-352a-72c7-8e78-5c52f6f14137_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term debt</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_019ca069-c770-79f1-bce4-849a013e67f8_totalLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Long-term debt</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_label_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebt" xlink:to="lab_us-gaap_LongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Assets_019c0c7d-352a-7168-925b-8c058f3d3c2e_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_AccruedInformationTechnologyPurchasesCurrent_019c07e0-213f-7249-9a41-371ac1d911d1_terseLabel_en-US" xlink:label="lab_blln_AccruedInformationTechnologyPurchasesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued information technology purchases</link:label>
    <link:label id="lab_blln_AccruedInformationTechnologyPurchasesCurrent_label_en-US" xlink:label="lab_blln_AccruedInformationTechnologyPurchasesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Information Technology Purchases, Current</link:label>
    <link:label id="lab_blln_AccruedInformationTechnologyPurchasesCurrent_documentation_en-US" xlink:label="lab_blln_AccruedInformationTechnologyPurchasesCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accrued Information Technology Purchases, Current</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_AccruedInformationTechnologyPurchasesCurrent" xlink:to="lab_blln_AccruedInformationTechnologyPurchasesCurrent" xlink:type="arc" order="1"/>
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    <link:label id="lab_blln_DebtInstrumentCovenantScheduleDomain_documentation_en-US" xlink:label="lab_blln_DebtInstrumentCovenantScheduleDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Covenant Schedule [Domain]</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxPolicyTextBlock_019c0e41-8a5a-725d-9d73-476d0071bd92_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax, Policy [Policy Text Block]</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_019c0d23-93a6-70e1-9420-faae7c78271a_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from operating activities:</link:label>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsResearch_019c65d5-e5fd-794a-8892-6bd5d2d32888_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsResearch" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Research and development credits</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsResearch" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsResearch"/>
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    <link:label id="lab_blln_DebtInstrumentRevenueParticipationAgreementMaximumAnnualNetRevenue_label_en-US" xlink:label="lab_blln_DebtInstrumentRevenueParticipationAgreementMaximumAnnualNetRevenue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Revenue Participation Agreement, Maximum Annual Net Revenue</link:label>
    <link:label id="lab_blln_DebtInstrumentRevenueParticipationAgreementMaximumAnnualNetRevenue_documentation_en-US" xlink:label="lab_blln_DebtInstrumentRevenueParticipationAgreementMaximumAnnualNetRevenue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Revenue Participation Agreement, Maximum Annual Net Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_DebtInstrumentRevenueParticipationAgreementMaximumAnnualNetRevenue" xlink:href="blln-20251231.xsd#blln_DebtInstrumentRevenueParticipationAgreementMaximumAnnualNetRevenue"/>
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    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_019c12da-1251-7a57-872b-359df0fb2105_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current assets:</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsFairValueDisclosureAbstract"/>
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    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths_019c08d3-a35e-7305-88a8-179ba156afb4_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
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    <link:label id="lab_us-gaap_WarrantMember_019ca01f-63b9-757d-a9cc-8010965127c9_terseLabel_en-US" xlink:label="lab_us-gaap_WarrantMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrant</link:label>
    <link:label id="lab_us-gaap_WarrantMember_label_en-US" xlink:label="lab_us-gaap_WarrantMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrant [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WarrantMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WarrantMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WarrantMember" xlink:to="lab_us-gaap_WarrantMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_019c0cb2-8c5f-74b5-b0a6-d39aae7735c3_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
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    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_019c0a42-e665-7cb8-abd4-7b2a696e6bb6_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 2</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel2Member" xlink:to="lab_us-gaap_FairValueInputsLevel2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFinStmtErrorCorrectionFlag_019c0cbd-223c-7340-b39c-d4c52f0bb813_terseLabel_en-US" xlink:label="lab_dei_DocumentFinStmtErrorCorrectionFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Financial Statement Error Correction [Flag]</link:label>
    <link:label id="lab_dei_DocumentFinStmtErrorCorrectionFlag_label_en-US" xlink:label="lab_dei_DocumentFinStmtErrorCorrectionFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Financial Statement Error Correction [Flag]</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes_019c0e8b-a755-7eec-b54b-0493511bdf5e_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">State and local income taxes, net of federal benefits</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, State and Local Income Taxes, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes"/>
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    <link:label id="lab_us-gaap_TemporaryEquityParOrStatedValuePerShare_019c0c7d-352a-757a-aa2b-a702be6e779a_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redeemable convertible preferred stock, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Par or Stated Value Per Share</link:label>
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    <link:label id="lab_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_019c6651-8d25-7686-9cee-6fd1fce441db_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year ending December 31:</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Fiscal Year Maturity [Abstract]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyMember" xlink:to="lab_us-gaap_RelatedPartyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_AccruedClinicalExpensesCurrent_019c07e6-7c7b-7f93-ba9b-b48c1acc13d8_terseLabel_en-US" xlink:label="lab_blln_AccruedClinicalExpensesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued clinical expenses</link:label>
    <link:label id="lab_blln_AccruedClinicalExpensesCurrent_label_en-US" xlink:label="lab_blln_AccruedClinicalExpensesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Clinical Expenses, Current</link:label>
    <link:label id="lab_blln_AccruedClinicalExpensesCurrent_documentation_en-US" xlink:label="lab_blln_AccruedClinicalExpensesCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accrued Clinical Expenses, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_AccruedClinicalExpensesCurrent" xlink:href="blln-20251231.xsd#blln_AccruedClinicalExpensesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_AccruedClinicalExpensesCurrent" xlink:to="lab_blln_AccruedClinicalExpensesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PlanNameAxis_019c139b-2737-7055-b400-9ecc66cf97e3_terseLabel_en-US" xlink:label="lab_us-gaap_PlanNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Plan Name [Axis]</link:label>
    <link:label id="lab_us-gaap_PlanNameAxis_label_en-US" xlink:label="lab_us-gaap_PlanNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Plan Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PlanNameAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PlanNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PlanNameAxis" xlink:to="lab_us-gaap_PlanNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_SeriesB2RedeemableConvertiblePreferredStockMember_019c0887-a6e4-7f9c-876b-915b81a02bac_terseLabel_en-US" xlink:label="lab_blln_SeriesB2RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series B-2</link:label>
    <link:label id="lab_blln_SeriesB2RedeemableConvertiblePreferredStockMember_label_en-US" xlink:label="lab_blln_SeriesB2RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series B-2 Redeemable Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_blln_SeriesB2RedeemableConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_blln_SeriesB2RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series B-2 Redeemable Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_SeriesB2RedeemableConvertiblePreferredStockMember" xlink:href="blln-20251231.xsd#blln_SeriesB2RedeemableConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_SeriesB2RedeemableConvertiblePreferredStockMember" xlink:to="lab_blln_SeriesB2RedeemableConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_019c0e1b-9d7c-7e97-b7f8-5af402337da2_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property and Equipment, Net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentInformationTable_019c0cb2-8c5f-709b-9432-45cd22ffa4c3_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Table]</link:label>
    <link:label id="lab_dei_DocumentInformationTable_label_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Information [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentInformationTable" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentInformationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentInformationTable" xlink:to="lab_dei_DocumentInformationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoMember_terseLabel_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO</link:label>
    <link:label id="lab_ecd_PeoMember_label_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoMember" xlink:to="lab_ecd_PeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract_019c0d23-93a7-7a0b-b079-40f396ebf043_terseLabel_en-US" xlink:label="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental non-cash investing and financing activities:</link:label>
    <link:label id="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract_label_en-US" xlink:label="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncash Investing and Financing Items [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoncashInvestingAndFinancingItemsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:to="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeInterest_019c0c8b-30ae-752e-a08f-086d886f1ac5_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest income</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeInterest_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income, Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeInterest" xlink:to="lab_us-gaap_InvestmentIncomeInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionLineItems_019c0e8f-e36a-7c0f-bf38-361ba9334a41_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Paid, by Individual Jurisdiction [Line Items]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionLineItems_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Paid, by Individual Jurisdiction [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPaidByIndividualJurisdictionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPaidByIndividualJurisdictionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxPaidByIndividualJurisdictionLineItems" xlink:to="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_country_US_019c662f-940c-7200-a924-7d6f2e270203_terseLabel_en-US" xlink:label="lab_country_US" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">UNITED STATES</link:label>
    <link:label id="lab_country_US_label_en-US" xlink:label="lab_country_US" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">UNITED STATES</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_US" xlink:href="https://xbrl.sec.gov/country/2025/country-2025.xsd#country_US"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_US" xlink:to="lab_country_US" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_A2022LSACommonStockWarrantsMember_019c12bb-9e5a-77a8-9dc3-b59c2dbccc3c_terseLabel_en-US" xlink:label="lab_blln_A2022LSACommonStockWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2022 LSA Amendment</link:label>
    <link:label id="lab_blln_A2022LSACommonStockWarrantsMember_label_en-US" xlink:label="lab_blln_A2022LSACommonStockWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2022 LSA Common Stock Warrants [Member]</link:label>
    <link:label id="lab_blln_A2022LSACommonStockWarrantsMember_documentation_en-US" xlink:label="lab_blln_A2022LSACommonStockWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2022 LSA Common Stock Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_A2022LSACommonStockWarrantsMember" xlink:href="blln-20251231.xsd#blln_A2022LSACommonStockWarrantsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_A2022LSACommonStockWarrantsMember" xlink:to="lab_blln_A2022LSACommonStockWarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance_019c0e8b-a755-7579-a92a-bad8344103bf_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in valuation allowance</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Change in Deferred Tax Assets Valuation Allowance, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:to="lab_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputSharePriceMember_019c0a54-7f44-7512-98e1-35b4c238f45e_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputSharePriceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock price (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_MeasurementInputSharePriceMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputSharePriceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Share Price [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputSharePriceMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputSharePriceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputSharePriceMember" xlink:to="lab_us-gaap_MeasurementInputSharePriceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment_019c0e80-d2c2-7a40-a292-d5864295bf3a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Property, Plant and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:to="lab_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsMember_019c0cdd-5616-7736-9a67-bb1214190b67_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Deficit</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsMember_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RetainedEarningsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsMember" xlink:to="lab_us-gaap_RetainedEarningsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityAxis_019c0e8f-e36a-7151-abd9-e15aeb0f3286_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction [Axis]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityAxis_label_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxAuthorityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxAuthorityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxAuthorityAxis" xlink:to="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019c0d23-93a7-7348-841c-cb9825fbc173_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents at beginning of year</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019c0d23-93a7-728e-9e08-8d0c9dc1d005_periodEndLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents at end of year</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementAbstract" xlink:to="lab_us-gaap_IncomeStatementAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_019c12b4-622c-764a-8e07-19a1ca252eed_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_label_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SaleOfStockNameOfTransactionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TaxesPayableCurrent_019c07dd-df79-70de-aa89-98f0412d1a49_terseLabel_en-US" xlink:label="lab_us-gaap_TaxesPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued property and other taxes</link:label>
    <link:label id="lab_us-gaap_TaxesPayableCurrent_label_en-US" xlink:label="lab_us-gaap_TaxesPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Taxes Payable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TaxesPayableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TaxesPayableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TaxesPayableCurrent" xlink:to="lab_us-gaap_TaxesPayableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues_019c0cdd-5616-713a-abf8-ab19e9ce5906_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of redeemable convertible preferred stock, net of issuance costs</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Stock Issued During Period, Value, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues" xlink:to="lab_us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_LoansPayableToBankAmortizationPeriod_019c78e5-b4ae-74a3-a7af-5c1cf13a5f53_terseLabel_en-US" xlink:label="lab_blln_LoansPayableToBankAmortizationPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization period</link:label>
    <link:label id="lab_blln_LoansPayableToBankAmortizationPeriod_label_en-US" xlink:label="lab_blln_LoansPayableToBankAmortizationPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Payable to Bank, Amortization Period</link:label>
    <link:label id="lab_blln_LoansPayableToBankAmortizationPeriod_documentation_en-US" xlink:label="lab_blln_LoansPayableToBankAmortizationPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loans Payable to Bank, Amortization Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_LoansPayableToBankAmortizationPeriod" xlink:href="blln-20251231.xsd#blln_LoansPayableToBankAmortizationPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_LoansPayableToBankAmortizationPeriod" xlink:to="lab_blln_LoansPayableToBankAmortizationPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputExpectedDividendRateMember_019c0a57-813e-72f8-8982-168a049a2de3_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputExpectedDividendRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividend yield</link:label>
    <link:label id="lab_us-gaap_MeasurementInputExpectedDividendRateMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputExpectedDividendRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Expected Dividend Rate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputExpectedDividendRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputExpectedDividendRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputExpectedDividendRateMember" xlink:to="lab_us-gaap_MeasurementInputExpectedDividendRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductsAndServicesDomain_019c128c-ba42-79c6-8268-036f7af190e6_terseLabel_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:label id="lab_srt_ProductsAndServicesDomain_label_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductsAndServicesDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProductsAndServicesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductsAndServicesDomain" xlink:to="lab_srt_ProductsAndServicesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationLiabilityTransfersOutOfLevel3_019c9005-28f8-7b2b-b88f-ee7403eb5eff_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationLiabilityTransfersOutOfLevel3" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Transfers from Level 3 to Level 2</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationLiabilityTransfersOutOfLevel3_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationLiabilityTransfersOutOfLevel3" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Liability, Transfers out of Level 3</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationLiabilityTransfersOutOfLevel3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationLiabilityTransfersOutOfLevel3"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationLiabilityTransfersOutOfLevel3" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationLiabilityTransfersOutOfLevel3" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_TemporaryEquitySharesConversionOfConvertibleSecurities_019c0cde-370c-7088-996b-57bf42a8beca_terseLabel_en-US" xlink:label="lab_blln_TemporaryEquitySharesConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion of redeemable convertible preferred stock to common stock in connection with initial public offering (in shares)</link:label>
    <link:label id="lab_blln_TemporaryEquitySharesConversionOfConvertibleSecurities_label_en-US" xlink:label="lab_blln_TemporaryEquitySharesConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Shares, Conversion Of Convertible Securities</link:label>
    <link:label id="lab_blln_TemporaryEquitySharesConversionOfConvertibleSecurities_documentation_en-US" xlink:label="lab_blln_TemporaryEquitySharesConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Shares, Conversion Of Convertible Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_TemporaryEquitySharesConversionOfConvertibleSecurities" xlink:href="blln-20251231.xsd#blln_TemporaryEquitySharesConversionOfConvertibleSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_TemporaryEquitySharesConversionOfConvertibleSecurities" xlink:to="lab_blln_TemporaryEquitySharesConversionOfConvertibleSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_LossOnExtinguishmentOfDebtUnamortizedDebtIssuanceCosts_019c12bb-9e5a-7518-a7c5-fff7216f0f0d_terseLabel_en-US" xlink:label="lab_blln_LossOnExtinguishmentOfDebtUnamortizedDebtIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unamortized debt issuance costs</link:label>
    <link:label id="lab_blln_LossOnExtinguishmentOfDebtUnamortizedDebtIssuanceCosts_label_en-US" xlink:label="lab_blln_LossOnExtinguishmentOfDebtUnamortizedDebtIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss on Extinguishment of Debt, Unamortized Debt Issuance Costs</link:label>
    <link:label id="lab_blln_LossOnExtinguishmentOfDebtUnamortizedDebtIssuanceCosts_documentation_en-US" xlink:label="lab_blln_LossOnExtinguishmentOfDebtUnamortizedDebtIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loss on Extinguishment of Debt, Unamortized Debt Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_LossOnExtinguishmentOfDebtUnamortizedDebtIssuanceCosts" xlink:href="blln-20251231.xsd#blln_LossOnExtinguishmentOfDebtUnamortizedDebtIssuanceCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_LossOnExtinguishmentOfDebtUnamortizedDebtIssuanceCosts" xlink:to="lab_blln_LossOnExtinguishmentOfDebtUnamortizedDebtIssuanceCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice_019c139b-2737-74a5-aedb-72b3a10c7a25_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vested and exercisable (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Exercisable, Weighted Average Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConversionOfStockAmountIssued1_019c0d66-66e6-7ffb-876f-b215af6edcd0_terseLabel_en-US" xlink:label="lab_us-gaap_ConversionOfStockAmountIssued1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion of redeemable convertible preferred stock into shares of Class A common stock in connection with the Company&#8217;s initial public offering</link:label>
    <link:label id="lab_us-gaap_ConversionOfStockAmountIssued1_label_en-US" xlink:label="lab_us-gaap_ConversionOfStockAmountIssued1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Conversion of Stock, Amount Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConversionOfStockAmountIssued1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConversionOfStockAmountIssued1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConversionOfStockAmountIssued1" xlink:to="lab_us-gaap_ConversionOfStockAmountIssued1" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_terseLabel_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement does not require Recovery</link:label>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_label_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Does Not Require Recovery [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RestatementDoesNotRequireRecoveryTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:to="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosure_019c12dc-dca2-7ef5-8e70-a32c16ac0c26_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesFairValueDisclosure" xlink:to="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_019c65ee-572f-7e91-91c2-4c88b3135157_terseLabel_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Description of Business</link:label>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:to="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable_019c0e8f-ccf5-772e-8c0c-f9664e7b89c9_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Paid, by Individual Jurisdiction [Table]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Paid, by Individual Jurisdiction [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPaidByIndividualJurisdictionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable" xlink:to="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CityAreaCode_019c0cb2-8c5f-7864-91ce-ca96553a0ac3_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CityAreaCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CityAreaCode" xlink:to="lab_dei_CityAreaCode" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgHowMnpiCnsdrdTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:to="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements_019c1e8d-c71d-71d8-b1ae-d3cf9f69b232_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Settlements</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Settlements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_019c0d23-93a6-7616-a794-dcf25af0e485_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from investing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTable_terseLabel_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure</link:label>
    <link:label id="lab_ecd_PvpTable_label_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTable" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PvpTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTable" xlink:to="lab_ecd_PvpTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:to="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SellingGeneralAndAdministrativeExpensesMember_019c139b-2738-7f3e-8c0b-e6f706211d4a_terseLabel_en-US" xlink:label="lab_us-gaap_SellingGeneralAndAdministrativeExpensesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Selling, general and administrative</link:label>
    <link:label id="lab_us-gaap_SellingGeneralAndAdministrativeExpensesMember_label_en-US" xlink:label="lab_us-gaap_SellingGeneralAndAdministrativeExpensesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Selling, General and Administrative Expenses [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SellingGeneralAndAdministrativeExpensesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SellingGeneralAndAdministrativeExpensesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SellingGeneralAndAdministrativeExpensesMember" xlink:to="lab_us-gaap_SellingGeneralAndAdministrativeExpensesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseCost_019c08e1-6076-7564-83e9-6545bd4a135b_totalLabel_en-US" xlink:label="lab_us-gaap_LeaseCost" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total finance lease cost</link:label>
    <link:label id="lab_us-gaap_LeaseCost_label_en-US" xlink:label="lab_us-gaap_LeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseCost" xlink:to="lab_us-gaap_LeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AutomobilesMember_019c09fd-3c41-7756-b4d9-1b40babeab90_terseLabel_en-US" xlink:label="lab_us-gaap_AutomobilesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Automobiles</link:label>
    <link:label id="lab_us-gaap_AutomobilesMember_label_en-US" xlink:label="lab_us-gaap_AutomobilesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Automobiles [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AutomobilesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AutomobilesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AutomobilesMember" xlink:to="lab_us-gaap_AutomobilesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseCostTableTextBlock_019c08b4-1e47-7d92-9bf9-91db4629589f_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseCostTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Other Information Related to Operating Leases</link:label>
    <link:label id="lab_us-gaap_LeaseCostTableTextBlock_label_en-US" xlink:label="lab_us-gaap_LeaseCostTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease, Cost [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseCostTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeaseCostTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseCostTableTextBlock" xlink:to="lab_us-gaap_LeaseCostTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit_019c0e76-2c67-717c-9cad-64fd57cd184e_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal</link:label>
    <link:label id="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Federal Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredFederalIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReconciliationOfUnrecognizedTaxBenefitsExcludingAmountsPertainingToExaminedTaxReturnsRollForward_019c0e93-e714-7274-9694-de915b65d384_terseLabel_en-US" xlink:label="lab_us-gaap_ReconciliationOfUnrecognizedTaxBenefitsExcludingAmountsPertainingToExaminedTaxReturnsRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecognized Tax Benefits [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_ReconciliationOfUnrecognizedTaxBenefitsExcludingAmountsPertainingToExaminedTaxReturnsRollForward_label_en-US" xlink:label="lab_us-gaap_ReconciliationOfUnrecognizedTaxBenefitsExcludingAmountsPertainingToExaminedTaxReturnsRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecognized Tax Benefits [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReconciliationOfUnrecognizedTaxBenefitsExcludingAmountsPertainingToExaminedTaxReturnsRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReconciliationOfUnrecognizedTaxBenefitsExcludingAmountsPertainingToExaminedTaxReturnsRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReconciliationOfUnrecognizedTaxBenefitsExcludingAmountsPertainingToExaminedTaxReturnsRollForward" xlink:to="lab_us-gaap_ReconciliationOfUnrecognizedTaxBenefitsExcludingAmountsPertainingToExaminedTaxReturnsRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AuditorName_019c1eac-a0dc-7818-ac5a-c5f3c476086a_terseLabel_en-US" xlink:label="lab_dei_AuditorName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Auditor Name</link:label>
    <link:label id="lab_dei_AuditorName_label_en-US" xlink:label="lab_dei_AuditorName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Auditor Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AuditorName" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AuditorName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AuditorName" xlink:to="lab_dei_AuditorName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_019c0d23-93a7-7d8a-9774-d08eabc2baf2_terseLabel_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental cash flow disclosure:</link:label>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_label_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Supplemental Cash Flow Information [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SupplementalCashFlowInformationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:to="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_label_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OtherPerfMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OtherPerfMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OtherPerfMeasureAmt" xlink:to="lab_ecd_OtherPerfMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward_019c139b-2737-7667-a7ce-2995bc49f852_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average Exercise Price Per Share</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Exercise Price [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDebtIssuanceCosts_019c0d23-93a7-7652-a18d-7a67e685d4fb_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payment of debt issuance costs on term loan</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDebtIssuanceCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Debt Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfDebtIssuanceCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:to="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Dividends_019c660c-1e8c-71eb-b621-ee361c0aa43f_terseLabel_en-US" xlink:label="lab_us-gaap_Dividends" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends declared or paid</link:label>
    <link:label id="lab_us-gaap_Dividends_label_en-US" xlink:label="lab_us-gaap_Dividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Dividends" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Dividends"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Dividends" xlink:to="lab_us-gaap_Dividends" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyDomain_019c124f-2694-76e9-8af7-7b0a8da60254_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyDomain" xlink:to="lab_us-gaap_RelatedPartyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract_019c65d0-5300-7f7b-8ecf-ca342ade89e1_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amount</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit), Effective Income Tax Rate Reconciliation, Amount [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:to="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OverAllotmentOptionMember_019c12b4-e208-7d53-977c-2d663556f6d2_terseLabel_en-US" xlink:label="lab_us-gaap_OverAllotmentOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Over-Allotment Option</link:label>
    <link:label id="lab_us-gaap_OverAllotmentOptionMember_label_en-US" xlink:label="lab_us-gaap_OverAllotmentOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Over-Allotment Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OverAllotmentOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OverAllotmentOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OverAllotmentOptionMember" xlink:to="lab_us-gaap_OverAllotmentOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VestingAxis_019c139b-2737-7553-a5ec-1680719c1723_terseLabel_en-US" xlink:label="lab_us-gaap_VestingAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting [Axis]</link:label>
    <link:label id="lab_us-gaap_VestingAxis_label_en-US" xlink:label="lab_us-gaap_VestingAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vesting [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VestingAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VestingAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VestingAxis" xlink:to="lab_us-gaap_VestingAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy_019c0e16-fedc-74ad-82c4-9cbc713cec8c_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value of Financial Instruments</link:label>
    <link:label id="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy_label_en-US" xlink:label="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value of Financial Instruments, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueOfFinancialInstrumentsPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:to="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeFinanceLeasesTextBlock_019c08af-d362-7d57-8691-030de76098ba_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeFinanceLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases</link:label>
    <link:label id="lab_us-gaap_LesseeFinanceLeasesTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeFinanceLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Finance Leases [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeFinanceLeasesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeFinanceLeasesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeFinanceLeasesTextBlock" xlink:to="lab_us-gaap_LesseeFinanceLeasesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_SeriesA5RedeemableConvertiblePreferredStockMember_019c0887-a6e4-74b1-829d-a24d0ce9dbed_terseLabel_en-US" xlink:label="lab_blln_SeriesA5RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series A-5</link:label>
    <link:label id="lab_blln_SeriesA5RedeemableConvertiblePreferredStockMember_label_en-US" xlink:label="lab_blln_SeriesA5RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series A-5 Redeemable Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_blln_SeriesA5RedeemableConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_blln_SeriesA5RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series A-5 Redeemable Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_SeriesA5RedeemableConvertiblePreferredStockMember" xlink:href="blln-20251231.xsd#blln_SeriesA5RedeemableConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_SeriesA5RedeemableConvertiblePreferredStockMember" xlink:to="lab_blln_SeriesA5RedeemableConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_DeferredTaxAssetsCapitalizedResearchAndDevelopment_019c0e7c-9f7c-7fd8-a72c-c8283b350dfd_terseLabel_en-US" xlink:label="lab_blln_DeferredTaxAssetsCapitalizedResearchAndDevelopment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capitalized R&amp;D expenditure</link:label>
    <link:label id="lab_blln_DeferredTaxAssetsCapitalizedResearchAndDevelopment_label_en-US" xlink:label="lab_blln_DeferredTaxAssetsCapitalizedResearchAndDevelopment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Capitalized Research And Development</link:label>
    <link:label id="lab_blln_DeferredTaxAssetsCapitalizedResearchAndDevelopment_documentation_en-US" xlink:label="lab_blln_DeferredTaxAssetsCapitalizedResearchAndDevelopment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Capitalized Research And Development</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_DeferredTaxAssetsCapitalizedResearchAndDevelopment" xlink:href="blln-20251231.xsd#blln_DeferredTaxAssetsCapitalizedResearchAndDevelopment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_DeferredTaxAssetsCapitalizedResearchAndDevelopment" xlink:to="lab_blln_DeferredTaxAssetsCapitalizedResearchAndDevelopment" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_DebtInstrumentCovenantScheduleAxis_019c12bb-9e5a-70c6-98b3-3bb250f594b4_terseLabel_en-US" xlink:label="lab_blln_DebtInstrumentCovenantScheduleAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Covenant Schedule [Axis]</link:label>
    <link:label id="lab_blln_DebtInstrumentCovenantScheduleAxis_label_en-US" xlink:label="lab_blln_DebtInstrumentCovenantScheduleAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Covenant Schedule [Axis]</link:label>
    <link:label id="lab_blln_DebtInstrumentCovenantScheduleAxis_documentation_en-US" xlink:label="lab_blln_DebtInstrumentCovenantScheduleAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Covenant Schedule</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_DebtInstrumentCovenantScheduleAxis" xlink:href="blln-20251231.xsd#blln_DebtInstrumentCovenantScheduleAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_DebtInstrumentCovenantScheduleAxis" xlink:to="lab_blln_DebtInstrumentCovenantScheduleAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_019c0d23-93a7-766d-b31f-3062649b4c8f_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by (used in) investing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1_019c1e7f-c0a7-7ca1-915a-119d90ce14a4_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remaining performance obligation, expected timing of satisfaction, period</link:label>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1_label_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1" xlink:to="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPaidNet_019c0d23-93a7-7f71-8a2f-6534530a38ab_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash payments for interest</link:label>
    <link:label id="lab_us-gaap_InterestPaidNet_label_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Paid, Excluding Capitalized Interest, Operating Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPaidNet" xlink:to="lab_us-gaap_InterestPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalYearFocus_019c0cb2-8c5f-71d8-b00b-366e2b321e2e_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalYearFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalYearFocus" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFiscalYearFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalYearFocus" xlink:to="lab_dei_DocumentFiscalYearFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_019c09df-ccf4-74c4-b3bf-efe2114d6796_terseLabel_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basis of Presentation</link:label>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Basis of Accounting, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BasisOfAccountingPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:to="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_019c0941-7311-75ae-97f6-d37006718573_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease right-of-use assets, net</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseRightOfUseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:to="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_OncologyMember_019c128c-ba42-792a-9742-557c83b0b32f_terseLabel_en-US" xlink:label="lab_blln_OncologyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Oncology</link:label>
    <link:label id="lab_blln_OncologyMember_label_en-US" xlink:label="lab_blln_OncologyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Oncology [Member]</link:label>
    <link:label id="lab_blln_OncologyMember_documentation_en-US" xlink:label="lab_blln_OncologyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Oncology</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_OncologyMember" xlink:href="blln-20251231.xsd#blln_OncologyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_OncologyMember" xlink:to="lab_blln_OncologyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedEmployeeBenefitsCurrent_019c0c7d-352a-7cce-943a-43c98e7b520e_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedEmployeeBenefitsCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued compensation and employee benefits</link:label>
    <link:label id="lab_us-gaap_AccruedEmployeeBenefitsCurrent_label_en-US" xlink:label="lab_us-gaap_AccruedEmployeeBenefitsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Employee Benefits, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedEmployeeBenefitsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccruedEmployeeBenefitsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedEmployeeBenefitsCurrent" xlink:to="lab_us-gaap_AccruedEmployeeBenefitsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations_019c65d7-602c-76a3-afb2-91ec18057c35_totalLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total provision for income taxes</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateContinuingOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseCost_019c0979-8e90-71e7-a895-1c168997b018_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, cost</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseCost_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseCost" xlink:to="lab_us-gaap_OperatingLeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PlanNameDomain_019c139b-2737-7629-9364-52e15a6af7d7_terseLabel_en-US" xlink:label="lab_us-gaap_PlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Plan Name [Domain]</link:label>
    <link:label id="lab_us-gaap_PlanNameDomain_label_en-US" xlink:label="lab_us-gaap_PlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Plan Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PlanNameDomain" xlink:to="lab_us-gaap_PlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_019c139b-2737-75d8-9f4d-d95a94e7e70a_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recognition period for unrecognized compensation cost</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:to="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_DebtCovenantTrancheOneMember_019c12bb-9e5a-7337-a5fe-c582cc540005_terseLabel_en-US" xlink:label="lab_blln_DebtCovenantTrancheOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">First Tranche</link:label>
    <link:label id="lab_blln_DebtCovenantTrancheOneMember_label_en-US" xlink:label="lab_blln_DebtCovenantTrancheOneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Covenant, Tranche One [Member]</link:label>
    <link:label id="lab_blln_DebtCovenantTrancheOneMember_documentation_en-US" xlink:label="lab_blln_DebtCovenantTrancheOneMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Covenant, Tranche One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_DebtCovenantTrancheOneMember" xlink:href="blln-20251231.xsd#blln_DebtCovenantTrancheOneMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_DebtCovenantTrancheOneMember" xlink:to="lab_blln_DebtCovenantTrancheOneMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_019c6578-50e3-7303-8877-f9e4553fbe4a_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common stock upon exercise of stock options (in shares)</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsValuationAllowance_019c6632-9949-76f1-8c97-b5710fd8ae6b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: valuation allowance</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsValuationAllowance_019cd08a-ebf6-71e8-adce-f4689a0f74c3_periodStartLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Valuation allowance - beginning of period</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsValuationAllowance_019cd08b-14c9-7155-85bb-0fee3d0c8b69_periodEndLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Valuation allowance - end of period</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsValuationAllowance_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Valuation Allowance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsValuationAllowance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:to="lab_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityAbstract_019c0c7d-352a-7e51-a50c-e1fef15372a5_terseLabel_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stockholders&#8217; equity:</link:label>
    <link:label id="lab_us-gaap_EquityAbstract_label_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Abstract]</link:label>
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    <link:label id="lab_us-gaap_BuildingMember_019c664d-36ff-7987-b8b6-01102d1a4415_terseLabel_en-US" xlink:label="lab_us-gaap_BuildingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Building</link:label>
    <link:label id="lab_us-gaap_BuildingMember_label_en-US" xlink:label="lab_us-gaap_BuildingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Building [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BuildingMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BuildingMember"/>
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    <link:label id="lab_blln_LossOnExtinguishmentOfDebtIncrementalExpense_019c12bb-9e5a-7276-b79b-f75db8ae29c2_terseLabel_en-US" xlink:label="lab_blln_LossOnExtinguishmentOfDebtIncrementalExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Incremental expense</link:label>
    <link:label id="lab_blln_LossOnExtinguishmentOfDebtIncrementalExpense_label_en-US" xlink:label="lab_blln_LossOnExtinguishmentOfDebtIncrementalExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss on Extinguishment of Debt, Incremental Expense</link:label>
    <link:label id="lab_blln_LossOnExtinguishmentOfDebtIncrementalExpense_documentation_en-US" xlink:label="lab_blln_LossOnExtinguishmentOfDebtIncrementalExpense" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loss on Extinguishment of Debt, Incremental Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_LossOnExtinguishmentOfDebtIncrementalExpense" xlink:href="blln-20251231.xsd#blln_LossOnExtinguishmentOfDebtIncrementalExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_LossOnExtinguishmentOfDebtIncrementalExpense" xlink:to="lab_blln_LossOnExtinguishmentOfDebtIncrementalExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_DebtInstrumentCovenantTrailingSixMonthGrossMarginMinimum_019c12bb-9e5a-7692-a72e-7d89a1590a9e_terseLabel_en-US" xlink:label="lab_blln_DebtInstrumentCovenantTrailingSixMonthGrossMarginMinimum" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Threshold, trailing six-month gross margin, minimum</link:label>
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    <link:label id="lab_blln_DebtInstrumentCovenantTrailingSixMonthGrossMarginMinimum_documentation_en-US" xlink:label="lab_blln_DebtInstrumentCovenantTrailingSixMonthGrossMarginMinimum" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Covenant, Trailing Six-Month Gross Margin, Minimum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_DebtInstrumentCovenantTrailingSixMonthGrossMarginMinimum" xlink:href="blln-20251231.xsd#blln_DebtInstrumentCovenantTrailingSixMonthGrossMarginMinimum"/>
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    <link:label id="lab_us-gaap_DeferredCompensationShareBasedArrangementsLiabilityCurrent_019ca04f-2ae8-761b-b35e-d54e70edb872_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredCompensationShareBasedArrangementsLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation liability</link:label>
    <link:label id="lab_us-gaap_DeferredCompensationShareBasedArrangementsLiabilityCurrent_label_en-US" xlink:label="lab_us-gaap_DeferredCompensationShareBasedArrangementsLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Compensation Share-Based Arrangements, Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredCompensationShareBasedArrangementsLiabilityCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredCompensationShareBasedArrangementsLiabilityCurrent"/>
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    <link:label id="lab_us-gaap_CurrentFederalTaxExpenseBenefit_019c0e76-2c67-7473-824d-b2f214368a32_terseLabel_en-US" xlink:label="lab_us-gaap_CurrentFederalTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal</link:label>
    <link:label id="lab_us-gaap_CurrentFederalTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_CurrentFederalTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Federal Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CurrentFederalTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CurrentFederalTaxExpenseBenefit"/>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_019c0cdd-5616-7e61-a119-01636df56904_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward"/>
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    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return [Text Block]</link:label>
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    <link:label id="lab_us-gaap_LesseeLeasesPolicyTextBlock_019c0e1f-0fd6-7359-aaaf-c79cdb864f49_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeLeasesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases</link:label>
    <link:label id="lab_us-gaap_LesseeLeasesPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeLeasesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Leases [Policy Text Block]</link:label>
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    <link:label id="lab_us-gaap_SellingGeneralAndAdministrativeExpense_019c0c8b-30ae-7c4d-bac4-b5c91884922d_terseLabel_en-US" xlink:label="lab_us-gaap_SellingGeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Selling, general and administrative</link:label>
    <link:label id="lab_us-gaap_SellingGeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_SellingGeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Selling, General and Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SellingGeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SellingGeneralAndAdministrativeExpense"/>
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    <link:label id="lab_us-gaap_MeasurementInputPriceVolatilityMember_019c0a55-1a36-77c4-b9f1-86f64fd3a88c_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputPriceVolatilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Volatility</link:label>
    <link:label id="lab_us-gaap_MeasurementInputPriceVolatilityMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputPriceVolatilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Price Volatility [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputPriceVolatilityMember" xlink:to="lab_us-gaap_MeasurementInputPriceVolatilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodValue_019c139b-2737-7dc8-bcb9-52f1b28b89ac_terseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Value of shares repurchased</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodValue_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased During Period, Value</link:label>
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    <link:label id="lab_blln_DeferredTaxAssetsLeaseLiabilities_019c0e7c-9f7c-7a2a-9d5b-3db059310e9f_terseLabel_en-US" xlink:label="lab_blln_DeferredTaxAssetsLeaseLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease liability</link:label>
    <link:label id="lab_blln_DeferredTaxAssetsLeaseLiabilities_label_en-US" xlink:label="lab_blln_DeferredTaxAssetsLeaseLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Lease Liabilities</link:label>
    <link:label id="lab_blln_DeferredTaxAssetsLeaseLiabilities_documentation_en-US" xlink:label="lab_blln_DeferredTaxAssetsLeaseLiabilities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amount before allocation of valuation allowances of deferred tax asset attributable to deductible temporary differences from lease liabilities.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_DeferredTaxAssetsLeaseLiabilities" xlink:href="blln-20251231.xsd#blln_DeferredTaxAssetsLeaseLiabilities"/>
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    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_019c0a00-d8e0-7b96-b05c-4f9232b78482_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization expense</link:label>
    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_label_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation, Depletion and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationDepletionAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DepreciationDepletionAndAmortization"/>
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    <link:label id="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction_019c1e71-468e-762e-9216-54f10bba9912_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net proceeds from sale of stock</link:label>
    <link:label id="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction_label_en-US" xlink:label="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Consideration Received on Transaction</link:label>
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    <link:label id="lab_us-gaap_IncrementalCommonSharesAttributableToConversionOfDebtSecurities_label_en-US" xlink:label="lab_us-gaap_IncrementalCommonSharesAttributableToConversionOfDebtSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Incremental Common Shares Attributable to Dilutive Effect of Conversion of Debt Securities</link:label>
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    <link:label id="lab_us-gaap_TradeAndOtherAccountsReceivablePolicy_019c0e18-6bbf-79c0-a5f5-5b4530e5400b_terseLabel_en-US" xlink:label="lab_us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts Receivable and Allowances</link:label>
    <link:label id="lab_us-gaap_TradeAndOtherAccountsReceivablePolicy_label_en-US" xlink:label="lab_us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TradeAndOtherAccountsReceivablePolicy"/>
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    <link:label id="lab_us-gaap_IncomeTaxReconciliationForeignIncomeTaxRateDifferential_019cada7-d43a-73dd-bf46-b634b648208d_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationForeignIncomeTaxRateDifferential" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign tax effects</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationForeignIncomeTaxRateDifferential_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationForeignIncomeTaxRateDifferential" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Foreign Income Tax Rate Differential, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationForeignIncomeTaxRateDifferential" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationForeignIncomeTaxRateDifferential"/>
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    <link:label id="lab_us-gaap_FinanceLeaseLiability_019c08d6-e618-7ef8-922f-461987a62d6f_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Present value of financing lease liabilities</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiability_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiability" xlink:to="lab_us-gaap_FinanceLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrDuration_terseLabel_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arrangement Duration</link:label>
    <link:label id="lab_ecd_TrdArrDuration_label_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Duration</link:label>
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    <link:label id="lab_us-gaap_PaymentOfFinancingAndStockIssuanceCosts_019c1e60-ed7a-7104-a39c-9318abc9b382_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentOfFinancingAndStockIssuanceCosts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payments of deferred offering costs</link:label>
    <link:label id="lab_us-gaap_PaymentOfFinancingAndStockIssuanceCosts_label_en-US" xlink:label="lab_us-gaap_PaymentOfFinancingAndStockIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment of Financing and Stock Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentOfFinancingAndStockIssuanceCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentOfFinancingAndStockIssuanceCosts"/>
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    <link:label id="lab_us-gaap_ComputerEquipmentMember_019c09fb-4450-7da0-9fda-491f7e7150e8_terseLabel_en-US" xlink:label="lab_us-gaap_ComputerEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Computer hardware</link:label>
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    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value by Liability Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain"/>
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    <link:label id="lab_dei_LocalPhoneNumber_019c0cb2-8c5f-7c45-a0e3-764028bcc1f7_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
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    <link:label id="lab_us-gaap_SharePrice_019c1e02-7edf-7321-a455-998fccc6ad5e_terseLabel_en-US" xlink:label="lab_us-gaap_SharePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate price (in dollars per share)</link:label>
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    <link:label id="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased and Retired During Period, Shares</link:label>
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    <link:label id="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt_019c0c8b-30ae-77bf-bae8-63df17f712f7_terseLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net gain on extinguishment of debt</link:label>
    <link:label id="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt_019c0d23-93a6-7118-b6dc-3dc05305b788_negatedLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Net gain on extinguishment of debt</link:label>
    <link:label id="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt_019c12bb-9e5a-70d1-ac55-a872d8e7ccb4_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Loss on extinguishment of debt</link:label>
    <link:label id="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt_label_en-US" xlink:label="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Extinguishment of Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainsLossesOnExtinguishmentOfDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:to="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_ValuationAllowanceRollForward_019cd08a-9c82-7d7b-a8cc-c5e4b2dd78e1_terseLabel_en-US" xlink:label="lab_blln_ValuationAllowanceRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Allowance [Roll Forward]</link:label>
    <link:label id="lab_blln_ValuationAllowanceRollForward_label_en-US" xlink:label="lab_blln_ValuationAllowanceRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Allowance [Roll Forward]</link:label>
    <link:label id="lab_blln_ValuationAllowanceRollForward_documentation_en-US" xlink:label="lab_blln_ValuationAllowanceRollForward" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Valuation Allowance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_ValuationAllowanceRollForward" xlink:href="blln-20251231.xsd#blln_ValuationAllowanceRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_ValuationAllowanceRollForward" xlink:to="lab_blln_ValuationAllowanceRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_PromissoryNotesReceivableTerm_019c6629-e49d-7b9d-9a24-be1e857c94bc_terseLabel_en-US" xlink:label="lab_blln_PromissoryNotesReceivableTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Promissory notes receivable, term</link:label>
    <link:label id="lab_blln_PromissoryNotesReceivableTerm_label_en-US" xlink:label="lab_blln_PromissoryNotesReceivableTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Promissory Notes Receivable, Term</link:label>
    <link:label id="lab_blln_PromissoryNotesReceivableTerm_documentation_en-US" xlink:label="lab_blln_PromissoryNotesReceivableTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Promissory Notes Receivable, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_PromissoryNotesReceivableTerm" xlink:href="blln-20251231.xsd#blln_PromissoryNotesReceivableTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_PromissoryNotesReceivableTerm" xlink:to="lab_blln_PromissoryNotesReceivableTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ExecutiveOfficerMember_019c1e73-5922-7f68-9737-52ab4f2784bf_terseLabel_en-US" xlink:label="lab_srt_ExecutiveOfficerMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Executive Officer</link:label>
    <link:label id="lab_srt_ExecutiveOfficerMember_label_en-US" xlink:label="lab_srt_ExecutiveOfficerMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Executive Officer [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ExecutiveOfficerMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ExecutiveOfficerMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ExecutiveOfficerMember" xlink:to="lab_srt_ExecutiveOfficerMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesCurrent_019cad91-2445-7267-a6eb-fadd53f13a44_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock warrant liability</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilitiesCurrent" xlink:to="lab_us-gaap_DerivativeLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_ClassOfWarrantOrRightRightToReturnWarrantsToCompanyCashValue_019c12bb-9e5a-7da1-956a-6a62e6fcca91_terseLabel_en-US" xlink:label="lab_blln_ClassOfWarrantOrRightRightToReturnWarrantsToCompanyCashValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Right to return warrants to company, cash value</link:label>
    <link:label id="lab_blln_ClassOfWarrantOrRightRightToReturnWarrantsToCompanyCashValue_label_en-US" xlink:label="lab_blln_ClassOfWarrantOrRightRightToReturnWarrantsToCompanyCashValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Right To Return Warrants To Company, Cash Value</link:label>
    <link:label id="lab_blln_ClassOfWarrantOrRightRightToReturnWarrantsToCompanyCashValue_documentation_en-US" xlink:label="lab_blln_ClassOfWarrantOrRightRightToReturnWarrantsToCompanyCashValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Right To Return Warrants To Company, Cash Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_ClassOfWarrantOrRightRightToReturnWarrantsToCompanyCashValue" xlink:href="blln-20251231.xsd#blln_ClassOfWarrantOrRightRightToReturnWarrantsToCompanyCashValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_ClassOfWarrantOrRightRightToReturnWarrantsToCompanyCashValue" xlink:to="lab_blln_ClassOfWarrantOrRightRightToReturnWarrantsToCompanyCashValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage_019c139b-2737-7536-95db-d5ec3ff1e60c_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting percentage</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Rights, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage" xlink:to="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_019c1285-31dd-7bdb-9c91-e6fdb7b5223b_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, interest rate, stated percentage</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Stated Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock_019c1286-1bc4-78aa-8069-84f3db5ad062_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Disaggregation of Revenue</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from External Customers by Products and Services [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock" xlink:to="lab_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityNoncurrent_019c0c7d-352a-7e6c-85c6-670cfc7d34ea_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease liabilities, non-current</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityNoncurrent_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilityNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:to="lab_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityVoluntaryFilers_019c0cb6-a6a2-7057-9c79-063b06354737_terseLabel_en-US" xlink:label="lab_dei_EntityVoluntaryFilers" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Voluntary Filers</link:label>
    <link:label id="lab_dei_EntityVoluntaryFilers_label_en-US" xlink:label="lab_dei_EntityVoluntaryFilers" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Voluntary Filers</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityVoluntaryFilers" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityVoluntaryFilers"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityVoluntaryFilers" xlink:to="lab_dei_EntityVoluntaryFilers" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_SeriesA4RedeemableConvertiblePreferredStockMember_019c0887-a6e4-7cc9-a629-308375501408_terseLabel_en-US" xlink:label="lab_blln_SeriesA4RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series A-4</link:label>
    <link:label id="lab_blln_SeriesA4RedeemableConvertiblePreferredStockMember_label_en-US" xlink:label="lab_blln_SeriesA4RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series A-4 Redeemable Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_blln_SeriesA4RedeemableConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_blln_SeriesA4RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series A-4 Redeemable Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_SeriesA4RedeemableConvertiblePreferredStockMember" xlink:href="blln-20251231.xsd#blln_SeriesA4RedeemableConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_SeriesA4RedeemableConvertiblePreferredStockMember" xlink:to="lab_blln_SeriesA4RedeemableConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAbstract_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_019c0cb2-8c5f-7098-9823-177d4a43a195_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets_019c0d23-93a6-78d2-9438-9360234c1bfe_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other non-current assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Noncurrent Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOtherNoncurrentAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherNoncurrentAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquitySharesOutstanding_019c0898-c7c9-76d0-8a3e-0402e1edb238_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redeemable convertible preferred stock, outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesOutstanding_019c0cdd-5616-7f03-a05c-9ef617a0bc44_periodStartLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesOutstanding_019c0cdd-5616-710a-9d17-731b67e1b236_periodEndLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesOutstanding_019c0811-1015-742d-801c-ff5aa0a31803_verboseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Shares Outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesOutstanding_label_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquitySharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquitySharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquitySharesOutstanding" xlink:to="lab_us-gaap_TemporaryEquitySharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method</link:label>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_label_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_StkPrcOrTsrEstimationMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:to="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_DebtInstrumentRevenueParticipationAgreementPercentOfQuarterlyNetRevenue_019c12bb-9e5a-7e42-b32b-29d642e1fabe_terseLabel_en-US" xlink:label="lab_blln_DebtInstrumentRevenueParticipationAgreementPercentOfQuarterlyNetRevenue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue participation agreement, percent of quarterly net revenue</link:label>
    <link:label id="lab_blln_DebtInstrumentRevenueParticipationAgreementPercentOfQuarterlyNetRevenue_label_en-US" xlink:label="lab_blln_DebtInstrumentRevenueParticipationAgreementPercentOfQuarterlyNetRevenue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Revenue Participation Agreement, Percent Of Quarterly Net Revenue</link:label>
    <link:label id="lab_blln_DebtInstrumentRevenueParticipationAgreementPercentOfQuarterlyNetRevenue_documentation_en-US" xlink:label="lab_blln_DebtInstrumentRevenueParticipationAgreementPercentOfQuarterlyNetRevenue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Revenue Participation Agreement, Percent Of Quarterly Net Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_DebtInstrumentRevenueParticipationAgreementPercentOfQuarterlyNetRevenue" xlink:href="blln-20251231.xsd#blln_DebtInstrumentRevenueParticipationAgreementPercentOfQuarterlyNetRevenue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_DebtInstrumentRevenueParticipationAgreementPercentOfQuarterlyNetRevenue" xlink:to="lab_blln_DebtInstrumentRevenueParticipationAgreementPercentOfQuarterlyNetRevenue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber_019c139b-2737-7c6b-8184-1b9e12b8eb5f_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vested and exercisable (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Exercisable, Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember_019c12bb-9e5a-76a5-a9d3-a2addbb64539_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period Two</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period Two [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPeriodTwoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StateAndLocalTaxJurisdictionOtherMember_019c4d51-8ffc-7be9-8903-36fd3ae1d75d_terseLabel_en-US" xlink:label="lab_us-gaap_StateAndLocalTaxJurisdictionOtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_StateAndLocalTaxJurisdictionOtherMember_label_en-US" xlink:label="lab_us-gaap_StateAndLocalTaxJurisdictionOtherMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">State and Local Tax Jurisdiction, Other [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StateAndLocalTaxJurisdictionOtherMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StateAndLocalTaxJurisdictionOtherMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StateAndLocalTaxJurisdictionOtherMember" xlink:to="lab_us-gaap_StateAndLocalTaxJurisdictionOtherMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_019c12dc-75c4-7965-af12-644d70095c28_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsFairValueDisclosure" xlink:to="lab_us-gaap_AssetsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfOperatingSegments_019c128c-ce25-7237-8d75-38e17e164890_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of operating segments</link:label>
    <link:label id="lab_us-gaap_NumberOfOperatingSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Operating Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfOperatingSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfOperatingSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfOperatingSegments" xlink:to="lab_us-gaap_NumberOfOperatingSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MachineryAndEquipmentMember_019c09f6-68af-7a71-85d2-c0216e171f57_terseLabel_en-US" xlink:label="lab_us-gaap_MachineryAndEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Machinery and equipment</link:label>
    <link:label id="lab_us-gaap_MachineryAndEquipmentMember_label_en-US" xlink:label="lab_us-gaap_MachineryAndEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Machinery and Equipment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MachineryAndEquipmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MachineryAndEquipmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MachineryAndEquipmentMember" xlink:to="lab_us-gaap_MachineryAndEquipmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_019c1414-3ec5-76e8-86ef-73eb00abc9c5_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issued (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_019c124f-2694-7759-8615-d24d53c05b8a_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_DebtIssuanceCostsExpensedUponElectionOfFairValueOption_019c0d23-93a6-7e3f-b2cd-aef858d8a640_terseLabel_en-US" xlink:label="lab_blln_DebtIssuanceCostsExpensedUponElectionOfFairValueOption" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt issuance costs on term loan expensed upon election of fair value option</link:label>
    <link:label id="lab_blln_DebtIssuanceCostsExpensedUponElectionOfFairValueOption_label_en-US" xlink:label="lab_blln_DebtIssuanceCostsExpensedUponElectionOfFairValueOption" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs Expensed Upon Election of Fair Value Option</link:label>
    <link:label id="lab_blln_DebtIssuanceCostsExpensedUponElectionOfFairValueOption_documentation_en-US" xlink:label="lab_blln_DebtIssuanceCostsExpensedUponElectionOfFairValueOption" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs Expensed Upon Election of Fair Value Option</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_DebtIssuanceCostsExpensedUponElectionOfFairValueOption" xlink:href="blln-20251231.xsd#blln_DebtIssuanceCostsExpensedUponElectionOfFairValueOption"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_DebtIssuanceCostsExpensedUponElectionOfFairValueOption" xlink:to="lab_blln_DebtIssuanceCostsExpensedUponElectionOfFairValueOption" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDateAxis_terseLabel_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date:</link:label>
    <link:label id="lab_ecd_RestatementDateAxis_label_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDateAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RestatementDateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDateAxis" xlink:to="lab_ecd_RestatementDateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_PrenatalMember_019c128c-ba42-7242-9df5-ae9cefac35f6_terseLabel_en-US" xlink:label="lab_blln_PrenatalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prenatal</link:label>
    <link:label id="lab_blln_PrenatalMember_label_en-US" xlink:label="lab_blln_PrenatalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prenatal [Member]</link:label>
    <link:label id="lab_blln_PrenatalMember_documentation_en-US" xlink:label="lab_blln_PrenatalMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Prenatal</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_PrenatalMember" xlink:href="blln-20251231.xsd#blln_PrenatalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_PrenatalMember" xlink:to="lab_blln_PrenatalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseDebt_019c12bb-9e5a-7958-95da-d4d5072edff9_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest expense, debt</link:label>
    <link:label id="lab_us-gaap_InterestExpenseDebt_label_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseDebt" xlink:to="lab_us-gaap_InterestExpenseDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationChangeInEnactedTaxRate_019cada6-7ad0-7281-88ed-8b5614a6e7e7_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationChangeInEnactedTaxRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in tax laws or rates enacted in the current period</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationChangeInEnactedTaxRate_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationChangeInEnactedTaxRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Change in Enacted Tax Rate, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationChangeInEnactedTaxRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationChangeInEnactedTaxRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxReconciliationChangeInEnactedTaxRate" xlink:to="lab_us-gaap_IncomeTaxReconciliationChangeInEnactedTaxRate" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndName_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_TrdArrIndName_label_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndName" xlink:to="lab_ecd_TrdArrIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WarrantsAndRightsOutstandingMeasurementInput_019c0a53-cdd8-7a81-94f9-aca12fc75ad1_terseLabel_en-US" xlink:label="lab_us-gaap_WarrantsAndRightsOutstandingMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants and rights outstanding, measurement input</link:label>
    <link:label id="lab_us-gaap_WarrantsAndRightsOutstandingMeasurementInput_label_en-US" xlink:label="lab_us-gaap_WarrantsAndRightsOutstandingMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrants and Rights Outstanding, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WarrantsAndRightsOutstandingMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WarrantsAndRightsOutstandingMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WarrantsAndRightsOutstandingMeasurementInput" xlink:to="lab_us-gaap_WarrantsAndRightsOutstandingMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_019c1285-31dd-71e6-89cb-0470177de109_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, face amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Face Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFaceAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentFaceAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFaceAmount" xlink:to="lab_us-gaap_DebtInstrumentFaceAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityByClassOfStockTable_019c0811-1015-71e1-91c1-0f18ede40cff_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityByClassOfStockTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Temporary Equity, by Class of Stock [Table]</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityByClassOfStockTable_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityByClassOfStockTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, by Class of Stock [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityByClassOfStockTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityByClassOfStockTable"/>
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    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
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    <link:label id="lab_us-gaap_FairValueByLiabilityClassAxis_019c0a63-e3d8-7262-b97b-056d2fc922aa_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liability Class [Axis]</link:label>
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    <link:label id="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:to="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_terseLabel_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Executive Categories</link:label>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_label_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Executive Categories [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllExecutiveCategoriesMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllExecutiveCategoriesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllExecutiveCategoriesMember" xlink:to="lab_ecd_AllExecutiveCategoriesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_019c0e71-fb49-7ae1-afc6-800884110485_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Deferred Tax Assets and Liabilities</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Deferred Tax Assets and Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockValue_019c0c7d-352a-7810-9b0c-7985ec6a1928_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock value</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockValue" xlink:to="lab_us-gaap_CommonStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable_019c0a43-197d-74cc-9400-4fcd4eacb9c1_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_EPSBasicAndDilutedAbstract_019c0c8b-30ae-7fba-b8f4-022a5002a808_terseLabel_en-US" xlink:label="lab_blln_EPSBasicAndDilutedAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average shares used in calculating net income (loss) per share attributable to common stockholders, basic and diluted:</link:label>
    <link:label id="lab_blln_EPSBasicAndDilutedAbstract_label_en-US" xlink:label="lab_blln_EPSBasicAndDilutedAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">EPS, Basic and Diluted [Abstract]</link:label>
    <link:label id="lab_blln_EPSBasicAndDilutedAbstract_documentation_en-US" xlink:label="lab_blln_EPSBasicAndDilutedAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">EPS, Basic and Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_EPSBasicAndDilutedAbstract" xlink:href="blln-20251231.xsd#blln_EPSBasicAndDilutedAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_EPSBasicAndDilutedAbstract" xlink:to="lab_blln_EPSBasicAndDilutedAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_019c0c7d-352a-7890-ba19-9b96064ca921_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and contingencies (Note 7)</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingencies" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommitmentsAndContingencies"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingencies" xlink:to="lab_us-gaap_CommitmentsAndContingencies" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansPayableMember_019ca035-5888-7ae1-bb62-902c1e665176_terseLabel_en-US" xlink:label="lab_us-gaap_LoansPayableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans Payable</link:label>
    <link:label id="lab_us-gaap_LoansPayableMember_label_en-US" xlink:label="lab_us-gaap_LoansPayableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Payable [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansPayableMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansPayableMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansPayableMember" xlink:to="lab_us-gaap_LoansPayableMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract_019c124b-3c67-7f59-a728-47220555424b_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Numerator:</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract"/>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsLiabilitiesNet_019c0e81-7b48-7ad0-9abc-b463d971ef9d_totalLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net deferred tax assets</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsLiabilitiesNet_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsLiabilitiesNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:to="lab_us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_CommonStockNumberOfVotesPerShare_019c0889-413e-75fa-98a3-967b9ab1908f_terseLabel_en-US" xlink:label="lab_blln_CommonStockNumberOfVotesPerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, number of votes per share</link:label>
    <link:label id="lab_blln_CommonStockNumberOfVotesPerShare_label_en-US" xlink:label="lab_blln_CommonStockNumberOfVotesPerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Number of Votes Per Share</link:label>
    <link:label id="lab_blln_CommonStockNumberOfVotesPerShare_documentation_en-US" xlink:label="lab_blln_CommonStockNumberOfVotesPerShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock, Number of Votes Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_CommonStockNumberOfVotesPerShare" xlink:href="blln-20251231.xsd#blln_CommonStockNumberOfVotesPerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_CommonStockNumberOfVotesPerShare" xlink:to="lab_blln_CommonStockNumberOfVotesPerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_TermLoanMember_019c0a6d-f903-7e33-a3a4-2f4940afe9c2_terseLabel_en-US" xlink:label="lab_blln_TermLoanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Term Loan</link:label>
    <link:label id="lab_blln_TermLoanMember_label_en-US" xlink:label="lab_blln_TermLoanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Term Loan [Member]</link:label>
    <link:label id="lab_blln_TermLoanMember_documentation_en-US" xlink:label="lab_blln_TermLoanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Term Loan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_TermLoanMember" xlink:href="blln-20251231.xsd#blln_TermLoanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_TermLoanMember" xlink:to="lab_blln_TermLoanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_label_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoActuallyPaidCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeoActuallyPaidCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoActuallyPaidCompAmt" xlink:to="lab_ecd_PeoActuallyPaidCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_IssuanceOfRedeemableConvertiblePreferredStockUponSettlementOfConvertibleNotes_019c0d23-93a7-7f8d-842b-3103299e38a9_terseLabel_en-US" xlink:label="lab_blln_IssuanceOfRedeemableConvertiblePreferredStockUponSettlementOfConvertibleNotes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of Series C-1 redeemable convertible preferred stock upon settlement of convertible notes</link:label>
    <link:label id="lab_blln_IssuanceOfRedeemableConvertiblePreferredStockUponSettlementOfConvertibleNotes_label_en-US" xlink:label="lab_blln_IssuanceOfRedeemableConvertiblePreferredStockUponSettlementOfConvertibleNotes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Issuance Of Redeemable Convertible Preferred Stock Upon Settlement Of Convertible Notes</link:label>
    <link:label id="lab_blln_IssuanceOfRedeemableConvertiblePreferredStockUponSettlementOfConvertibleNotes_documentation_en-US" xlink:label="lab_blln_IssuanceOfRedeemableConvertiblePreferredStockUponSettlementOfConvertibleNotes" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Issuance Of Redeemable Convertible Preferred Stock Upon Settlement Of Convertible Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_IssuanceOfRedeemableConvertiblePreferredStockUponSettlementOfConvertibleNotes" xlink:href="blln-20251231.xsd#blln_IssuanceOfRedeemableConvertiblePreferredStockUponSettlementOfConvertibleNotes"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod_019c139b-2737-73fd-a2e6-e93c8fe1ffa3_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Forfeited or expired (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Forfeitures and Expirations in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareDilutedAbstract_019c124b-3c67-771a-9264-4f0424a3fefc_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDilutedAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted net income (loss) per share:</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDilutedAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDilutedAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDilutedAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareDilutedAbstract"/>
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    <link:label id="lab_us-gaap_ScheduleOfUnrecognizedTaxBenefitsRollForwardTableTextBlock_019c0e72-2aeb-7e15-b5b9-db45429cbe6e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfUnrecognizedTaxBenefitsRollForwardTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Reconciliation of Unrecognized Tax Benefits</link:label>
    <link:label id="lab_us-gaap_ScheduleOfUnrecognizedTaxBenefitsRollForwardTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfUnrecognizedTaxBenefitsRollForwardTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Unrecognized Tax Benefits Roll Forward [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfUnrecognizedTaxBenefitsRollForwardTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfUnrecognizedTaxBenefitsRollForwardTableTextBlock"/>
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    <link:label id="lab_us-gaap_AccountsPayableAndOtherAccruedLiabilitiesCurrent_019c07e9-1f9d-7c66-b72c-17ca5c7f8c45_totalLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableAndOtherAccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses and other current liabilities</link:label>
    <link:label id="lab_us-gaap_AccountsPayableAndOtherAccruedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsPayableAndOtherAccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable and Other Accrued Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableAndOtherAccruedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsPayableAndOtherAccruedLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableAndOtherAccruedLiabilitiesCurrent" xlink:to="lab_us-gaap_AccountsPayableAndOtherAccruedLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_019c1e72-29a4-71b1-9051-c31096cfe4b8_verboseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Gross proceeds from sale of stock</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromIssuanceOfCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_AccruedInventoryPurchasesCurrent_019c07d6-1a6c-7087-9770-4eab896f710e_terseLabel_en-US" xlink:label="lab_blln_AccruedInventoryPurchasesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued inventory purchases</link:label>
    <link:label id="lab_blln_AccruedInventoryPurchasesCurrent_label_en-US" xlink:label="lab_blln_AccruedInventoryPurchasesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Inventory Purchases, Current</link:label>
    <link:label id="lab_blln_AccruedInventoryPurchasesCurrent_documentation_en-US" xlink:label="lab_blln_AccruedInventoryPurchasesCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accrued Inventory Purchases, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_AccruedInventoryPurchasesCurrent" xlink:href="blln-20251231.xsd#blln_AccruedInventoryPurchasesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_AccruedInventoryPurchasesCurrent" xlink:to="lab_blln_AccruedInventoryPurchasesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllIndividualsMember_terseLabel_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Individuals</link:label>
    <link:label id="lab_ecd_AllIndividualsMember_label_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Individuals [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllIndividualsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllIndividualsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="lab_ecd_AllIndividualsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_019c1285-31dd-7bcb-a3bc-a226b874db72_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeDomain" xlink:to="lab_us-gaap_LongtermDebtTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_019c0d23-93a6-7062-961c-730a270cb381_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of property and equipment</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:to="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryIndName" xlink:to="lab_ecd_ForgoneRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_019c139b-2737-7cf4-86b7-994f9ceabff4_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expiration period</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Expiration Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xlink:to="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_label_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:to="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent_019c139b-2737-709e-9130-1efd0ec5dbc9_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchase price of common stock, percent of market price</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Purchase Price of Common Stock, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:to="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputExercisePriceMember_019c0a53-cdd8-750b-bdc8-10ecc46fac0f_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputExercisePriceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise price (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_MeasurementInputExercisePriceMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputExercisePriceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Exercise Price [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputExercisePriceMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputExercisePriceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputExercisePriceMember" xlink:to="lab_us-gaap_MeasurementInputExercisePriceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_The2025ESPPMember_019c1435-16be-7c5f-b1ea-b8be12ae2144_terseLabel_en-US" xlink:label="lab_blln_The2025ESPPMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">The 2025 ESPP</link:label>
    <link:label id="lab_blln_The2025ESPPMember_label_en-US" xlink:label="lab_blln_The2025ESPPMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">The 2025 ESPP [Member]</link:label>
    <link:label id="lab_blln_The2025ESPPMember_documentation_en-US" xlink:label="lab_blln_The2025ESPPMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The 2025 Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_The2025ESPPMember" xlink:href="blln-20251231.xsd#blln_The2025ESPPMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_The2025ESPPMember" xlink:to="lab_blln_The2025ESPPMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromNotesPayable_019c12bb-9e5a-7dfd-b660-23fe822227e7_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromNotesPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from notes payable</link:label>
    <link:label id="lab_us-gaap_ProceedsFromNotesPayable_label_en-US" xlink:label="lab_us-gaap_ProceedsFromNotesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Notes Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromNotesPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromNotesPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromNotesPayable" xlink:to="lab_us-gaap_ProceedsFromNotesPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis</link:label>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_label_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompAnalysisTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ErrCompAnalysisTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompAnalysisTextBlock" xlink:to="lab_ecd_ErrCompAnalysisTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtConversionConvertedInstrumentSharesIssued1_019c1285-31dd-70b2-bd77-a5533fe7f5b0_terseLabel_en-US" xlink:label="lab_us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt conversion, converted instrument, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_DebtConversionConvertedInstrumentSharesIssued1_label_en-US" xlink:label="lab_us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Conversion, Converted Instrument, Shares Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtConversionConvertedInstrumentSharesIssued1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xlink:to="lab_us-gaap_DebtConversionConvertedInstrumentSharesIssued1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionLineItems_019c1eaf-a30d-71da-9ec7-52d2542479cd_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Line Items]</link:label>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionLineItems_label_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeLeaseDescriptionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeLeaseDescriptionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeLeaseDescriptionLineItems" xlink:to="lab_us-gaap_LesseeLeaseDescriptionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_Rule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:to="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_SeriesA6RedeemableConvertiblePreferredStockMember_019c0887-a6e4-7319-bb10-6656c7c97128_terseLabel_en-US" xlink:label="lab_blln_SeriesA6RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series A-6</link:label>
    <link:label id="lab_blln_SeriesA6RedeemableConvertiblePreferredStockMember_label_en-US" xlink:label="lab_blln_SeriesA6RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series A-6 Redeemable Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_blln_SeriesA6RedeemableConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_blln_SeriesA6RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series A-6 Redeemable Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_SeriesA6RedeemableConvertiblePreferredStockMember" xlink:href="blln-20251231.xsd#blln_SeriesA6RedeemableConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_SeriesA6RedeemableConvertiblePreferredStockMember" xlink:to="lab_blln_SeriesA6RedeemableConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ParticipatingSecuritiesDistributedAndUndistributedEarningsLossBasic_019c0c8b-30ae-7661-9dda-a66a73b3a7cf_negatedLabel_en-US" xlink:label="lab_us-gaap_ParticipatingSecuritiesDistributedAndUndistributedEarningsLossBasic" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Less: Net income (loss) attributable to participating securities</link:label>
    <link:label id="lab_us-gaap_ParticipatingSecuritiesDistributedAndUndistributedEarningsLossBasic_019c124b-3c67-761f-aed8-67048bcb5318_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ParticipatingSecuritiesDistributedAndUndistributedEarningsLossBasic" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: Net income attributable to participating securities</link:label>
    <link:label id="lab_us-gaap_ParticipatingSecuritiesDistributedAndUndistributedEarningsLossBasic_label_en-US" xlink:label="lab_us-gaap_ParticipatingSecuritiesDistributedAndUndistributedEarningsLossBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Participating Securities, Distributed and Undistributed Earnings (Loss), Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ParticipatingSecuritiesDistributedAndUndistributedEarningsLossBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ParticipatingSecuritiesDistributedAndUndistributedEarningsLossBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ParticipatingSecuritiesDistributedAndUndistributedEarningsLossBasic" xlink:to="lab_us-gaap_ParticipatingSecuritiesDistributedAndUndistributedEarningsLossBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompRecoveryTable_terseLabel_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery</link:label>
    <link:label id="lab_ecd_ErrCompRecoveryTable_label_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompRecoveryTable" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ErrCompRecoveryTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompRecoveryTable" xlink:to="lab_ecd_ErrCompRecoveryTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_Security12bTitle_019c0cb2-8c5f-77e9-abf4-1c1cee3ecd0d_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:label id="lab_dei_Security12bTitle_label_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_Security12bTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_Security12bTitle" xlink:to="lab_dei_Security12bTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableAggregateIntrinsicValue_019c139b-2737-74db-b70a-ad8176888c9b_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableAggregateIntrinsicValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate intrinsic value, vested and exercisable</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableAggregateIntrinsicValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableAggregateIntrinsicValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Exercisable, Aggregate Intrinsic Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableAggregateIntrinsicValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableAggregateIntrinsicValue"/>
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    <link:label id="lab_us-gaap_LesseeLeaseDescriptionTable_019c1eaf-a30d-78a4-9cc2-c0fb62aaf443_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Table]</link:label>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionTable_label_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeLeaseDescriptionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeLeaseDescriptionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeLeaseDescriptionTable" xlink:to="lab_us-gaap_LesseeLeaseDescriptionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityLiquidationPreference_019c083a-ff2e-7c3c-b45a-32bb8f83f950_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityLiquidationPreference" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redeemable convertible preferred stock, liquidation preference</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityLiquidationPreference_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityLiquidationPreference" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Liquidation Preference</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityLiquidationPreference" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityLiquidationPreference"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityLiquidationPreference" xlink:to="lab_us-gaap_TemporaryEquityLiquidationPreference" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract_019cc0d7-b00e-74fd-a572-b492dbd9633c_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive loss, net of taxes:</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Parent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_RedeemableConvertiblePreferredStockWarrantsMember_019ca020-baa4-739b-87c8-f172967238b6_verboseLabel_en-US" xlink:label="lab_blln_RedeemableConvertiblePreferredStockWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Redeemable Convertible Preferred Stock Warrants</link:label>
    <link:label id="lab_blln_RedeemableConvertiblePreferredStockWarrantsMember_019c124b-3c67-7224-93c0-8b53813c2c68_terseLabel_en-US" xlink:label="lab_blln_RedeemableConvertiblePreferredStockWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants to purchase redeemable convertible preferred stock</link:label>
    <link:label id="lab_blln_RedeemableConvertiblePreferredStockWarrantsMember_label_en-US" xlink:label="lab_blln_RedeemableConvertiblePreferredStockWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Redeemable Convertible Preferred Stock Warrants [Member]</link:label>
    <link:label id="lab_blln_RedeemableConvertiblePreferredStockWarrantsMember_documentation_en-US" xlink:label="lab_blln_RedeemableConvertiblePreferredStockWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Redeemable Convertible Preferred Stock Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_RedeemableConvertiblePreferredStockWarrantsMember" xlink:href="blln-20251231.xsd#blln_RedeemableConvertiblePreferredStockWarrantsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_RedeemableConvertiblePreferredStockWarrantsMember" xlink:to="lab_blln_RedeemableConvertiblePreferredStockWarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_019c0c8b-30ae-7f2d-a35c-7748e6d0c011_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) per share attributable to common stockholders, basic and diluted:</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareAbstract" xlink:to="lab_us-gaap_EarningsPerShareAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_019c08c5-80ff-7601-a779-c63d4745a262_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpense_019c0c8b-30ae-75c4-a6bc-b4a065c764a7_totalLabel_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total other income (expense)</link:label>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpense_label_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonoperating Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonoperatingIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NonoperatingIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonoperatingIncomeExpense" xlink:to="lab_us-gaap_NonoperatingIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_DebtInstrumentRedemptionPeriod_019c12bb-9e5a-7391-930a-6820f0e9077b_terseLabel_en-US" xlink:label="lab_blln_DebtInstrumentRedemptionPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, redemption period</link:label>
    <link:label id="lab_blln_DebtInstrumentRedemptionPeriod_label_en-US" xlink:label="lab_blln_DebtInstrumentRedemptionPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption Period</link:label>
    <link:label id="lab_blln_DebtInstrumentRedemptionPeriod_documentation_en-US" xlink:label="lab_blln_DebtInstrumentRedemptionPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_DebtInstrumentRedemptionPeriod" xlink:href="blln-20251231.xsd#blln_DebtInstrumentRedemptionPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_DebtInstrumentRedemptionPeriod" xlink:to="lab_blln_DebtInstrumentRedemptionPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_019c124b-3c67-7792-bbd2-77ea69e18f24_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:to="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_MeasurementInputExpectedTerm2Member_019c0a6f-2e15-71a0-ae61-7733f206258b_terseLabel_en-US" xlink:label="lab_blln_MeasurementInputExpectedTerm2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expected term (years) &#8211; Scenario 2</link:label>
    <link:label id="lab_blln_MeasurementInputExpectedTerm2Member_label_en-US" xlink:label="lab_blln_MeasurementInputExpectedTerm2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Expected Term 2 [Member]</link:label>
    <link:label id="lab_blln_MeasurementInputExpectedTerm2Member_documentation_en-US" xlink:label="lab_blln_MeasurementInputExpectedTerm2Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Expected Term 2</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_MeasurementInputExpectedTerm2Member" xlink:href="blln-20251231.xsd#blln_MeasurementInputExpectedTerm2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_MeasurementInputExpectedTerm2Member" xlink:to="lab_blln_MeasurementInputExpectedTerm2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability_019c0d23-93a6-70bc-b4e3-3208812b8645_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred revenue</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Contract with Customer, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInContractWithCustomerLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:to="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_TemporaryEquityValueConversionOfConvertibleSecurities_019c0cde-370c-7806-ad2f-cb53ae78ae01_terseLabel_en-US" xlink:label="lab_blln_TemporaryEquityValueConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion of redeemable convertible preferred stock to Class A and Class B common stock in connection with initial public offering</link:label>
    <link:label id="lab_blln_TemporaryEquityValueConversionOfConvertibleSecurities_label_en-US" xlink:label="lab_blln_TemporaryEquityValueConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Value, Conversion Of Convertible Securities</link:label>
    <link:label id="lab_blln_TemporaryEquityValueConversionOfConvertibleSecurities_documentation_en-US" xlink:label="lab_blln_TemporaryEquityValueConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Value, Conversion Of Convertible Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_TemporaryEquityValueConversionOfConvertibleSecurities" xlink:href="blln-20251231.xsd#blln_TemporaryEquityValueConversionOfConvertibleSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_TemporaryEquityValueConversionOfConvertibleSecurities" xlink:to="lab_blln_TemporaryEquityValueConversionOfConvertibleSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_OfferingCostIncludedInAccountsPayableAccruedExpensesAndOtherCurrentLiabilities_019c0d66-66e6-7dcb-bf60-4aa1294d5b91_terseLabel_en-US" xlink:label="lab_blln_OfferingCostIncludedInAccountsPayableAccruedExpensesAndOtherCurrentLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Offering costs in accounts payable and accrued expenses and other current liabilities</link:label>
    <link:label id="lab_blln_OfferingCostIncludedInAccountsPayableAccruedExpensesAndOtherCurrentLiabilities_label_en-US" xlink:label="lab_blln_OfferingCostIncludedInAccountsPayableAccruedExpensesAndOtherCurrentLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offering Cost Included In Accounts Payable Accrued Expenses And Other Current Liabilities</link:label>
    <link:label id="lab_blln_OfferingCostIncludedInAccountsPayableAccruedExpensesAndOtherCurrentLiabilities_documentation_en-US" xlink:label="lab_blln_OfferingCostIncludedInAccountsPayableAccruedExpensesAndOtherCurrentLiabilities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Offering Cost Included In Accounts Payable Accrued Expenses And Other Current Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_OfferingCostIncludedInAccountsPayableAccruedExpensesAndOtherCurrentLiabilities" xlink:href="blln-20251231.xsd#blln_OfferingCostIncludedInAccountsPayableAccruedExpensesAndOtherCurrentLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_OfferingCostIncludedInAccountsPayableAccruedExpensesAndOtherCurrentLiabilities" xlink:to="lab_blln_OfferingCostIncludedInAccountsPayableAccruedExpensesAndOtherCurrentLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredOfferingCosts_019c128c-ce25-72db-baae-561c242b51a0_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredOfferingCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred offering costs</link:label>
    <link:label id="lab_us-gaap_DeferredOfferingCosts_label_en-US" xlink:label="lab_us-gaap_DeferredOfferingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Offering Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredOfferingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredOfferingCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredOfferingCosts" xlink:to="lab_us-gaap_DeferredOfferingCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice_019c139b-2737-7362-ba7a-101ca1392c5b_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercised (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Exercises in Period, Weighted Average Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgDiscLineItems_label_en-US" xlink:label="lab_ecd_AwardTmgDiscLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Disclosures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgDiscLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgDiscLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgDiscLineItems" xlink:to="lab_ecd_AwardTmgDiscLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseRenewalTerm_019c0936-9599-7420-a862-7493f2b1698a_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseRenewalTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, renewal term</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseRenewalTerm_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseRenewalTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Renewal Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseRenewalTerm" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseRenewalTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseRenewalTerm" xlink:to="lab_us-gaap_LesseeOperatingLeaseRenewalTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_CommonStockConvertibleTerm_019c8ff6-8bf9-7385-864a-fd1a2c3f0bcc_terseLabel_en-US" xlink:label="lab_blln_CommonStockConvertibleTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, convertible, term</link:label>
    <link:label id="lab_blln_CommonStockConvertibleTerm_label_en-US" xlink:label="lab_blln_CommonStockConvertibleTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Convertible, Term</link:label>
    <link:label id="lab_blln_CommonStockConvertibleTerm_documentation_en-US" xlink:label="lab_blln_CommonStockConvertibleTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock, Convertible, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_CommonStockConvertibleTerm" xlink:href="blln-20251231.xsd#blln_CommonStockConvertibleTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_CommonStockConvertibleTerm" xlink:to="lab_blln_CommonStockConvertibleTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_019c0811-1015-7631-bfcc-e611034439ba_verboseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Redeemable Convertible Preferred Stock</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_019c139b-2737-7dd1-81a9-3d2280aa4721_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityNoteDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:to="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit_019c0e77-d402-78f2-9032-f1e262e67363_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">State</link:label>
    <link:label id="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred State and Local Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_IL_019c4d51-27f0-72a3-86c9-e63e5ed2c120_terseLabel_en-US" xlink:label="lab_stpr_IL" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Illinois</link:label>
    <link:label id="lab_stpr_IL_label_en-US" xlink:label="lab_stpr_IL" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">ILLINOIS</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_IL" xlink:href="https://xbrl.sec.gov/stpr/2025/stpr-2025.xsd#stpr_IL"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_IL" xlink:to="lab_stpr_IL" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLoss_019c0c8b-30ae-7968-820a-0672a3aad8d3_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net income (loss)</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_019c0cdd-5616-7197-8243-bf9e7781e5d2_netLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Net (loss) income</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_019c0d23-93a6-7235-ab53-5f4a28e22d33_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss)</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConstructionInProgressMember_019c09f6-68af-7800-803b-dc9e6d5f3dde_terseLabel_en-US" xlink:label="lab_us-gaap_ConstructionInProgressMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Construction in progress</link:label>
    <link:label id="lab_us-gaap_ConstructionInProgressMember_label_en-US" xlink:label="lab_us-gaap_ConstructionInProgressMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Construction in Progress [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConstructionInProgressMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConstructionInProgressMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConstructionInProgressMember" xlink:to="lab_us-gaap_ConstructionInProgressMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAccruedLiabilitiesCurrent_019c07e4-c6c2-7da6-b615-ebd9471d3312_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_OtherAccruedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Accrued Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAccruedLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:to="lab_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_019c0e72-12bd-7d80-972e-3d39600375e1_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Effective Income Tax Rate Reconciliation</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Effective Income Tax Rate Reconciliation [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_019c139b-2737-776a-b52c-56257631e36f_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting period</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_ChiefExecutiveOfficerAndCoFounderMember_019c139b-2737-7e3c-a7b6-4c2a72097e34_terseLabel_en-US" xlink:label="lab_blln_ChiefExecutiveOfficerAndCoFounderMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Chief Executive Officer And Co-Founder</link:label>
    <link:label id="lab_blln_ChiefExecutiveOfficerAndCoFounderMember_label_en-US" xlink:label="lab_blln_ChiefExecutiveOfficerAndCoFounderMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Chief Executive Officer And Co-Founder [Member]</link:label>
    <link:label id="lab_blln_ChiefExecutiveOfficerAndCoFounderMember_documentation_en-US" xlink:label="lab_blln_ChiefExecutiveOfficerAndCoFounderMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Chief Executive Officer And Co-Founder</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_ChiefExecutiveOfficerAndCoFounderMember" xlink:href="blln-20251231.xsd#blln_ChiefExecutiveOfficerAndCoFounderMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_ChiefExecutiveOfficerAndCoFounderMember" xlink:to="lab_blln_ChiefExecutiveOfficerAndCoFounderMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_019c0d23-93a7-7a12-8022-491f76d22583_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repurchase of common stock outstanding</link:label>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_label_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for Repurchase of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForRepurchaseOfCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:to="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrAdoptionDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adoption Date</link:label>
    <link:label id="lab_ecd_TrdArrAdoptionDate_label_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Adoption Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrAdoptionDate" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrAdoptionDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrAdoptionDate" xlink:to="lab_ecd_TrdArrAdoptionDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharesIssuedPricePerShare_019c661b-3ccd-72fd-be41-cbecce7adc1b_terseLabel_en-US" xlink:label="lab_us-gaap_SharesIssuedPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares issued, price (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_SharesIssuedPricePerShare_label_en-US" xlink:label="lab_us-gaap_SharesIssuedPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Issued, Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharesIssuedPricePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharesIssuedPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharesIssuedPricePerShare" xlink:to="lab_us-gaap_SharesIssuedPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseTermOfContract_019c1e9f-2981-75db-ba1b-f996fe66da15_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Term of contract</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseTermOfContract_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Term of Contract</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseTermOfContract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:to="lab_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityAggregateAmountOfRedemptionRequirement_019ca02b-d4a7-7ca8-99c7-b071bf023ba6_verboseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityAggregateAmountOfRedemptionRequirement" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Gross proceeds</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityAggregateAmountOfRedemptionRequirement_019c0811-1015-7c73-bded-ce1df59feb1f_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityAggregateAmountOfRedemptionRequirement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Liquidation Preference</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityAggregateAmountOfRedemptionRequirement_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityAggregateAmountOfRedemptionRequirement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Aggregate Amount of Redemption Requirement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityAggregateAmountOfRedemptionRequirement" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityAggregateAmountOfRedemptionRequirement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityAggregateAmountOfRedemptionRequirement" xlink:to="lab_us-gaap_TemporaryEquityAggregateAmountOfRedemptionRequirement" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputExpectedTermMember_019c0a6f-a6fc-719c-af99-a041097090d2_verboseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputExpectedTermMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Expected term (years) &#8211; Scenario 1</link:label>
    <link:label id="lab_us-gaap_MeasurementInputExpectedTermMember_019c0a58-b3e4-70c9-aea7-6a6129905cfd_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputExpectedTermMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expected term (years)</link:label>
    <link:label id="lab_us-gaap_MeasurementInputExpectedTermMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputExpectedTermMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Expected Term [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputExpectedTermMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputExpectedTermMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputExpectedTermMember" xlink:to="lab_us-gaap_MeasurementInputExpectedTermMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SellingGeneralAndAdministrativeExpensesPolicyTextBlock_019c0e40-e5bb-7b68-b65b-399c3cb22819_terseLabel_en-US" xlink:label="lab_us-gaap_SellingGeneralAndAdministrativeExpensesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Selling, General and Administrative</link:label>
    <link:label id="lab_us-gaap_SellingGeneralAndAdministrativeExpensesPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_SellingGeneralAndAdministrativeExpensesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Selling, General and Administrative Expenses, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SellingGeneralAndAdministrativeExpensesPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SellingGeneralAndAdministrativeExpensesPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SellingGeneralAndAdministrativeExpensesPolicyTextBlock" xlink:to="lab_us-gaap_SellingGeneralAndAdministrativeExpensesPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract_019c0d23-93a7-71bb-aaad-6ba60f38e96d_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from financing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Continuing Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_019c0c8b-30ae-7e3e-804d-247b5e77933b_totalLabel_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income (loss) from operations</link:label>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_label_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Income (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingIncomeLoss" xlink:to="lab_us-gaap_OperatingIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_019c0c7d-352a-75c9-9981-99df0c978521_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated deficit</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_019cb8f7-de15-763e-9252-9855a305c5d8_negatedLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Accumulated deficit</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:to="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock_019c0d23-93a7-73b8-9b7c-b5969dce6f12_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from issuance of Series D redeemable convertible preferred stock, net of issuance costs</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_terseLabel_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_label_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember"/>
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    <link:label id="lab_us-gaap_StatementClassOfStockAxis_019c0811-1015-7962-bb0e-069a956ffd71_terseLabel_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_label_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementClassOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementClassOfStockAxis" xlink:to="lab_us-gaap_StatementClassOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_PromissoryNotesReceivableStatedInterestRate_019c1e02-7edf-7de2-b5b1-ce108e3ce32a_terseLabel_en-US" xlink:label="lab_blln_PromissoryNotesReceivableStatedInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate (as a percent)</link:label>
    <link:label id="lab_blln_PromissoryNotesReceivableStatedInterestRate_label_en-US" xlink:label="lab_blln_PromissoryNotesReceivableStatedInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Promissory Notes Receivable, Stated Interest Rate</link:label>
    <link:label id="lab_blln_PromissoryNotesReceivableStatedInterestRate_documentation_en-US" xlink:label="lab_blln_PromissoryNotesReceivableStatedInterestRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Promissory Notes Receivable, Stated Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_PromissoryNotesReceivableStatedInterestRate" xlink:href="blln-20251231.xsd#blln_PromissoryNotesReceivableStatedInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_PromissoryNotesReceivableStatedInterestRate" xlink:to="lab_blln_PromissoryNotesReceivableStatedInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ImpairmentOfIntangibleAssetsFinitelived_019c6603-ce5e-7fce-8ef7-9ee2597eb653_terseLabel_en-US" xlink:label="lab_us-gaap_ImpairmentOfIntangibleAssetsFinitelived" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Impairment of intangible assets, finite-lived</link:label>
    <link:label id="lab_us-gaap_ImpairmentOfIntangibleAssetsFinitelived_label_en-US" xlink:label="lab_us-gaap_ImpairmentOfIntangibleAssetsFinitelived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impairment of Intangible Assets, Finite-Lived</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ImpairmentOfIntangibleAssetsFinitelived" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ImpairmentOfIntangibleAssetsFinitelived"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ImpairmentOfIntangibleAssetsFinitelived" xlink:to="lab_us-gaap_ImpairmentOfIntangibleAssetsFinitelived" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember"/>
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    <link:label id="lab_us-gaap_PayablesAndAccrualsAbstract_label_en-US" xlink:label="lab_us-gaap_PayablesAndAccrualsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payables and Accruals [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PayablesAndAccrualsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PayablesAndAccrualsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PayablesAndAccrualsAbstract" xlink:to="lab_us-gaap_PayablesAndAccrualsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_019c0c8b-30ae-7449-8a0c-0553877f1c71_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other expense, net</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_label_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Nonoperating Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherNonoperatingIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:to="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementTable_019c0c82-11c8-77eb-8c48-f4151047590d_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementTable" xlink:to="lab_us-gaap_StatementTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefit_019c0e76-2c67-732d-bf18-fedd6dba7970_totalLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Deferred income tax provision</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxExpenseBenefit"/>
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    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_019c0d23-93a6-74bc-b979-a09efa56921f_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustments to reconcile net income (loss) to net cash provided by (used in) operating activities:</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract"/>
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    <link:label id="lab_us-gaap_MeasurementInputRiskFreeInterestRateMember_019c0a57-5392-785a-9d66-50c0b718c865_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputRiskFreeInterestRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Risk-free rate</link:label>
    <link:label id="lab_us-gaap_MeasurementInputRiskFreeInterestRateMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputRiskFreeInterestRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Risk Free Interest Rate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputRiskFreeInterestRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputRiskFreeInterestRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputRiskFreeInterestRateMember" xlink:to="lab_us-gaap_MeasurementInputRiskFreeInterestRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerLiability_019c128c-ce25-71d7-afb3-f897c66829e8_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred revenue balance</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerLiability_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractWithCustomerLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerLiability" xlink:to="lab_us-gaap_ContractWithCustomerLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityNoncurrent_019c0c7d-352a-7a42-9d89-2e37dd5b38ce_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing lease liabilities, non-current</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityNoncurrent_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:to="lab_us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityFairValueDisclosure_019c1285-31dd-70da-8ce2-f459f977f9e5_terseLabel_en-US" xlink:label="lab_us-gaap_EquityFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity, fair value disclosure</link:label>
    <link:label id="lab_us-gaap_EquityFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_EquityFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityFairValueDisclosure" xlink:to="lab_us-gaap_EquityFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllAdjToCompMember_terseLabel_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation</link:label>
    <link:label id="lab_ecd_AllAdjToCompMember_label_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllAdjToCompMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllAdjToCompMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllAdjToCompMember" xlink:to="lab_ecd_AllAdjToCompMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AmendmentFlag_019c0cb2-8c5f-7bc0-915b-5859362dc615_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:label id="lab_dei_AmendmentFlag_label_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AmendmentFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AmendmentFlag" xlink:to="lab_dei_AmendmentFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_FairValueAdjustmentOfDebtInstruments_019c12ba-0aa9-735d-86f1-d71222707cd9_terseLabel_en-US" xlink:label="lab_blln_FairValueAdjustmentOfDebtInstruments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of debt agreements</link:label>
    <link:label id="lab_blln_FairValueAdjustmentOfDebtInstruments_label_en-US" xlink:label="lab_blln_FairValueAdjustmentOfDebtInstruments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Adjustment of Debt Instruments</link:label>
    <link:label id="lab_blln_FairValueAdjustmentOfDebtInstruments_documentation_en-US" xlink:label="lab_blln_FairValueAdjustmentOfDebtInstruments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value Adjustment of Debt Instruments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_FairValueAdjustmentOfDebtInstruments" xlink:href="blln-20251231.xsd#blln_FairValueAdjustmentOfDebtInstruments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_FairValueAdjustmentOfDebtInstruments" xlink:to="lab_blln_FairValueAdjustmentOfDebtInstruments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockPricePerShare_019c12b5-042f-7a38-a434-9aa77c21410c_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of stock price per share (in usd per share)</link:label>
    <link:label id="lab_us-gaap_SaleOfStockPricePerShare_label_en-US" xlink:label="lab_us-gaap_SaleOfStockPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockPricePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SaleOfStockPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockPricePerShare" xlink:to="lab_us-gaap_SaleOfStockPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_019c139b-2737-7fef-8da7-3fd0a0ecc5cb_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_UnsecuredConvertiblePromissoryNotesMember_019c1285-31dd-7f4d-9b52-4df2ad2249e6_terseLabel_en-US" xlink:label="lab_blln_UnsecuredConvertiblePromissoryNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unsecured Convertible Promissory Notes</link:label>
    <link:label id="lab_blln_UnsecuredConvertiblePromissoryNotesMember_label_en-US" xlink:label="lab_blln_UnsecuredConvertiblePromissoryNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Convertible Promissory Notes [Member]</link:label>
    <link:label id="lab_blln_UnsecuredConvertiblePromissoryNotesMember_documentation_en-US" xlink:label="lab_blln_UnsecuredConvertiblePromissoryNotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unsecured Convertible Promissory Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_UnsecuredConvertiblePromissoryNotesMember" xlink:href="blln-20251231.xsd#blln_UnsecuredConvertiblePromissoryNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_UnsecuredConvertiblePromissoryNotesMember" xlink:to="lab_blln_UnsecuredConvertiblePromissoryNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrTerminationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Termination Date</link:label>
    <link:label id="lab_ecd_TrdArrTerminationDate_label_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Termination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrTerminationDate" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrTerminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrTerminationDate" xlink:to="lab_ecd_TrdArrTerminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_InsiderTrdPoliciesProcAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:to="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_DebtCovenantTrancheDomain_019c1e09-4107-71a9-9a6d-9b199bf82e6b_terseLabel_en-US" xlink:label="lab_blln_DebtCovenantTrancheDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt, Covenant, Tranche [Domain]</link:label>
    <link:label id="lab_blln_DebtCovenantTrancheDomain_label_en-US" xlink:label="lab_blln_DebtCovenantTrancheDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt, Covenant, Tranche [Domain]</link:label>
    <link:label id="lab_blln_DebtCovenantTrancheDomain_documentation_en-US" xlink:label="lab_blln_DebtCovenantTrancheDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt, Covenant, Tranche [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_DebtCovenantTrancheDomain" xlink:href="blln-20251231.xsd#blln_DebtCovenantTrancheDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_DebtCovenantTrancheDomain" xlink:to="lab_blln_DebtCovenantTrancheDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_SeriesC1RedeemableConvertiblePreferredStockMember_019c0887-a6e4-784f-a6f6-563acd9ca250_terseLabel_en-US" xlink:label="lab_blln_SeriesC1RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series C-1</link:label>
    <link:label id="lab_blln_SeriesC1RedeemableConvertiblePreferredStockMember_label_en-US" xlink:label="lab_blln_SeriesC1RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series C-1 Redeemable Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_blln_SeriesC1RedeemableConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_blln_SeriesC1RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series C-1 Redeemable Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_SeriesC1RedeemableConvertiblePreferredStockMember" xlink:href="blln-20251231.xsd#blln_SeriesC1RedeemableConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_SeriesC1RedeemableConvertiblePreferredStockMember" xlink:to="lab_blln_SeriesC1RedeemableConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_blln_SeriesA1RedeemableConvertiblePreferredStockMember_019c0887-a6e4-7834-a78a-38813f50d311_terseLabel_en-US" xlink:label="lab_blln_SeriesA1RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series A-1</link:label>
    <link:label id="lab_blln_SeriesA1RedeemableConvertiblePreferredStockMember_label_en-US" xlink:label="lab_blln_SeriesA1RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series A-1 Redeemable Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_blln_SeriesA1RedeemableConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_blln_SeriesA1RedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Series A-1 Redeemable Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_SeriesA1RedeemableConvertiblePreferredStockMember" xlink:href="blln-20251231.xsd#blln_SeriesA1RedeemableConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blln_SeriesA1RedeemableConvertiblePreferredStockMember" xlink:to="lab_blln_SeriesA1RedeemableConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_019c096d-0936-782c-ba58-7200acb379c3_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, weighted average discount rate</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Weighted Average Discount Rate, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:to="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_019c139b-2737-70f3-8051-bf158f581ccd_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Stock Option Activity</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option, Activity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_019c0c8b-30ae-7d61-9fb0-fe4ac75c14c3_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average shares used in calculating net income (loss) per share, basic (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTable_019c139b-2738-7f6a-a5b0-643823f677ff_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Expensed and Capitalized, Amount [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Expensed and Capitalized, Amount [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTable" xlink:to="lab_us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTable" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_InventoryWriteDown_label_en-US" xlink:label="lab_us-gaap_InventoryWriteDown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory Write-down</link:label>
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    <link:label id="lab_us-gaap_UnrecognizedTaxBenefitsThatWouldImpactEffectiveTaxRate_019ca057-060f-7165-9ff4-3d30ef74a46b_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefitsThatWouldImpactEffectiveTaxRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecognized tax benefits that would impact the effective tax rate</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventsAbstract"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs"/>
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    <link:label id="lab_blln_SeriesARedeemableConvertiblePreferredStockMember_019c088c-b7dd-77d5-9107-c2a80e7cf23f_terseLabel_en-US" xlink:label="lab_blln_SeriesARedeemableConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series A</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems"/>
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    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_019c124b-3c67-7a63-ac3d-f09d9a21c2a2_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:to="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAxis_019c0a42-e665-7f7a-80d6-d7aa3c991ee3_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents [Axis]</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAxis_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents [Axis]</link:label>
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    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PnsnAdjsPrrSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:to="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrecognizedTaxBenefitsIncreasesResultingFromCurrentPeriodTaxPositions_019c0e94-301e-7c3f-a717-e4344a238914_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefitsIncreasesResultingFromCurrentPeriodTaxPositions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increases related to current year&#8217;s tax positions</link:label>
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    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_019c0cdd-5616-7c03-bf15-ca46430ae4e2_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of Class A common stock in connection with initial public offering, net of underwriting discounts and commissions and issuance costs</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues"/>
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    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodFiveMember_019c12bb-9e5a-7d73-b5f1-ee644e7b6541_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodFiveMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period Five</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodFiveMember_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodFiveMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period Five [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodFiveMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPeriodFiveMember"/>
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    <link:label id="lab_us-gaap_PaymentsForLeasingCosts_019c65ba-875e-7083-83c6-3a0b8c9a1fd7_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForLeasingCosts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Deposits paid for financing leases</link:label>
    <link:label id="lab_us-gaap_PaymentsForLeasingCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsForLeasingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for Leasing Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForLeasingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForLeasingCosts"/>
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    <link:label id="lab_blln_FairValueAdjustmentOfCommonStockWarrantLiability_019c0d23-93a6-7eca-9eb2-36d306481549_negatedTerseLabel_en-US" xlink:label="lab_blln_FairValueAdjustmentOfCommonStockWarrantLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of common stock warrant liability</link:label>
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    <link:label id="lab_blln_FairValueAdjustmentOfCommonStockWarrantLiability_documentation_en-US" xlink:label="lab_blln_FairValueAdjustmentOfCommonStockWarrantLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value Adjustment Of Common Stock Warrant Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blln_FairValueAdjustmentOfCommonStockWarrantLiability" xlink:href="blln-20251231.xsd#blln_FairValueAdjustmentOfCommonStockWarrantLiability"/>
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    <link:label id="lab_srt_CounterpartyNameAxis_019c12bb-9e5a-7121-93c2-7c60bc39544b_terseLabel_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Name [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_srt_CounterpartyNameAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_CounterpartyNameAxis"/>
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    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock_019c6619-dde4-704a-b1e2-fda93a375847_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Restricted Stock Unit Activity</link:label>
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    <link:label id="lab_us-gaap_ComponentsOfDeferredTaxLiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_ComponentsOfDeferredTaxLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Components of Deferred Tax Liabilities [Abstract]</link:label>
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