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    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerTextBlock_6c9e8ae9-ca14-4dc2-88ac-d17e9692b5fe_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">REVENUE FROM CONTRACTS WITH CUSTOMERS AND OTHER INCOME</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerTextBlock_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer [Text Block]</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract_1d1258de-6cdd-4130-903a-17f91e4bd36c_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableBeforeAllowanceForCreditLossAbstract"/>
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    <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>
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    <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"/>
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    <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"/>
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    <link:label id="lab_blue_NegotiableOrderOfWithdrawalNOWAndDemandDeposits_documentation_en-US" xlink:label="lab_blue_NegotiableOrderOfWithdrawalNOWAndDemandDeposits" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Negotiable Order of Withdrawal (NOW) And Demand Deposits</link:label>
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    <link:label id="lab_us-gaap_StockholdersEquity_4433d993-a000-4a0c-a793-c748462a16a8_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">Balance at end of period</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_9cc64dc5-21e1-4254-b2f4-100f9ee3602b_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total stockholders&#8217; equity</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>
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    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByMeasurementFrequencyAxis"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleTable_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Table]</link:label>
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    <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>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTextBlock_76ee8c82-7e4a-4dc8-b6e1-cb5a730daf16_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 premises and equipment, net</link:label>
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    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_ab556feb-05bf-4ca0-8533-ce9e8743b247_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>
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    <link:label id="lab_us-gaap_FairValueMeasurementsRecurringMember_ccbd22c0-1499-4204-b21d-eb7a1bceb0d4_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measured on a recurring basis:</link:label>
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    <link:label id="lab_blue_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsNonvestedOptionsExpiredWeightedAverageGrantDateFairValue_60333fd7-740c-422b-93fd-ce86f1fc3ea2_terseLabel_en-US" xlink:label="lab_blue_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsNonvestedOptionsExpiredWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expired (in dollars per share)</link:label>
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    <link:label id="lab_us-gaap_TierOneLeverageCapitalRequiredToBeWellCapitalized_aabe1879-1119-4fca-9030-fcb8d651854d_terseLabel_en-US" xlink:label="lab_us-gaap_TierOneLeverageCapitalRequiredToBeWellCapitalized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tier 1 (leverage) capital</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFinancingReceivableRecordedInvestmentCreditQualityIndicatorTable"/>
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    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019b50cf-3b41-7640-9414-cd057ca384d2_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Loss before income tax benefit</link:label>
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    <link:label id="lab_dei_EntityShellCompany_e8a4cb1d-0b28-4efc-9469-5d4ee5e16840_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>
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    <link:label id="lab_us-gaap_TierOneLeverageCapitalToAverageAssets_b0f1cf31-d9bf-4bd4-9b84-da25f154f270_terseLabel_en-US" xlink:label="lab_us-gaap_TierOneLeverageCapitalToAverageAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tier 1 (leverage) capital</link:label>
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    <link:label id="lab_blue_FinancingReceivablePurchasedLoansThresholdNumberOfDaysPastDueDelinquent_019c4273-0067-717e-bf77-517e1b2cbbeb_terseLabel_en-US" xlink:label="lab_blue_FinancingReceivablePurchasedLoansThresholdNumberOfDaysPastDueDelinquent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing receivable, purchased loans, threshold number of days past due, delinquent</link:label>
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    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue_145cf6ae-f408-4fcd-82a9-0e5ab39c43c7_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset-backed securities</link:label>
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    <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>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseRemainingLeaseTerm_974faa71-6b8a-4e54-973b-cc4a342c6d56_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseRemainingLeaseTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remaining lease terms</link:label>
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    <link:label id="lab_us-gaap_InterestIncomeSecuritiesMortgageBacked_7021d673-25ee-47e7-aadd-f95c4e60fc60_terseLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeSecuritiesMortgageBacked" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Taxable investment income</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseOperating"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanAccumulatedOtherComprehensiveIncomeNetPriorServiceCostCreditBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlanAccumulatedOtherComprehensiveIncomeNetPriorServiceCostCreditBeforeTax"/>
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    <link:label id="lab_us-gaap_InterestExpenseDomesticDeposits_240ad02e-31d8-49c8-bb47-de79b632389e_totalLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseDomesticDeposits" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_InterestExpenseDomesticDeposits_label_en-US" xlink:label="lab_us-gaap_InterestExpenseDomesticDeposits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Domestic Deposits</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseDomesticDeposits" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseDomesticDeposits"/>
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    <link:label id="lab_us-gaap_JuniorLienMember_01aabe68-632e-4a87-986e-395226f2b1cb_terseLabel_en-US" xlink:label="lab_us-gaap_JuniorLienMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Junior liens</link:label>
    <link:label id="lab_us-gaap_JuniorLienMember_label_en-US" xlink:label="lab_us-gaap_JuniorLienMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Junior Lien [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_JuniorLienMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_JuniorLienMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_JuniorLienMember" xlink:to="lab_us-gaap_JuniorLienMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable_21ea079a-b27e-4d0a-93fa-02e7c7acdf01_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income [Table]</link:label>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable_label_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTable"/>
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    <link:label id="lab_blue_FinancingReceivableExcludingAccruedInterestCollectivelyEvaluatedForImpairment_cb09077b-5cca-4bac-a71c-45971d1a3a60_terseLabel_en-US" xlink:label="lab_blue_FinancingReceivableExcludingAccruedInterestCollectivelyEvaluatedForImpairment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collectively Evaluated</link:label>
    <link:label id="lab_blue_FinancingReceivableExcludingAccruedInterestCollectivelyEvaluatedForImpairment_label_en-US" xlink:label="lab_blue_FinancingReceivableExcludingAccruedInterestCollectivelyEvaluatedForImpairment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Collectively Evaluated For Impairment</link:label>
    <link:label id="lab_blue_FinancingReceivableExcludingAccruedInterestCollectivelyEvaluatedForImpairment_documentation_en-US" xlink:label="lab_blue_FinancingReceivableExcludingAccruedInterestCollectivelyEvaluatedForImpairment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Collectively Evaluated For Impairment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blue_FinancingReceivableExcludingAccruedInterestCollectivelyEvaluatedForImpairment" xlink:href="blue-20251231.xsd#blue_FinancingReceivableExcludingAccruedInterestCollectivelyEvaluatedForImpairment"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlansAndOtherPostretirementBenefitPlansTableTextBlockLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlansAndOtherPostretirementBenefitPlansTableTextBlockLineItems"/>
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    <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"/>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual_1babba26-104d-46c7-92ae-33eea5aaabc0_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-accrual</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Nonaccrual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestNonaccrual" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FurnitureAndFixturesMember_2d49add0-1b49-4b66-a293-de05d103311c_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">Furnishings and equipment</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_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss_269b7020-c5f4-4d85-b0e4-10e43a2665da_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Excluding Accrued Interest, after Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AwardTypeAxis_2d172a5d-6695-47fb-88c0-13432ff19f38_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 [Axis]</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_HedgingRelationshipDomain_10b0f97a-fa12-4821-a816-e3c70ed88604_terseLabel_en-US" xlink:label="lab_us-gaap_HedgingRelationshipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging Relationship [Domain]</link:label>
    <link:label id="lab_us-gaap_HedgingRelationshipDomain_label_en-US" xlink:label="lab_us-gaap_HedgingRelationshipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedging Relationship [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingRelationshipDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HedgingRelationshipDomain"/>
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    <link:label id="lab_srt_ParentCompanyMember_129f2ed0-088f-47ac-a0d9-b800f119090e_terseLabel_en-US" xlink:label="lab_srt_ParentCompanyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Parent Company</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_srt_ParentCompanyMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ParentCompanyMember"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_e5e41637-4147-4e37-9a55-9fbe885ec7e9_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">Share-Based Compensation</link:label>
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    <link:label id="lab_dei_TradingSymbol_0fe990ae-8c19-4a03-9c3d-d48abe27b737_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>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_70981193-88a1-41f6-b8ec-dbd19e10b2c7_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>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsCharitableContributionCarryforwards_e23aafbc-af32-4ec8-b443-ba61677b93f4_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsCharitableContributionCarryforwards" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Charitable contribution carryover</link:label>
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    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_019bea73-f9ec-7139-91b3-e8c5f01f8ade_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">Options exercised</link:label>
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    <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>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanChangeInBenefitObligationRollForward_ab485c77-fcec-43be-b2e3-02ab0320221d_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanChangeInBenefitObligationRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in benefit obligation:</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityCreditQualityIndicatorLineItems_212952f7-5b2d-4563-b0a8-7e331120c3c5_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityCreditQualityIndicatorLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Credit Quality Indicator [Line Items]</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesHeldToMaturityCreditQualityIndicatorLineItems_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesHeldToMaturityCreditQualityIndicatorLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Credit Quality Indicator [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesHeldToMaturityCreditQualityIndicatorLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesHeldToMaturityCreditQualityIndicatorLineItems"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward_0130613e-849d-46d2-8014-7c5a4cb417d8_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of Shares Awarded</link:label>
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    <link:label id="lab_us-gaap_PledgedStatusDomain_d178b048-686f-4f9e-b4f6-1bcba42c1be7_terseLabel_en-US" xlink:label="lab_us-gaap_PledgedStatusDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pledged Status [Domain]</link:label>
    <link:label id="lab_us-gaap_PledgedStatusDomain_label_en-US" xlink:label="lab_us-gaap_PledgedStatusDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pledged Status [Domain]</link:label>
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    <link:label id="lab_dei_EntityAddressPostalZipCode_41d3f556-8392-49c5-b863-645a80317cd9_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>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDeterminationDate" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RestatementDeterminationDate"/>
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    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_badc7cd8-16d6-4ea0-b0b2-0d3213aa4966_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Income tax expense</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_23357c8f-afd5-46f0-9a6a-75e82314602c_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</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_0a7f9516-78f5-465f-bd0c-22f5d3685214_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Income tax expense</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_2087e68a-bb29-4e78-8b73-b2db40866769_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">Income tax benefit</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>
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    <link:label id="lab_us-gaap_OtherAssets_cb2f03c7-cb01-46f3-979f-37d709ab98f4_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
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    <link:label id="lab_blue_BlueFoundryBancorpNJMember_f42eff95-3e90-44fe-810f-cafc3174ac7e_terseLabel_en-US" xlink:label="lab_blue_BlueFoundryBancorpNJMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Blue Foundry Bancorp - NJ</link:label>
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    <link:label id="lab_blue_TreasuryStockSharesTransferredToRestrictedStockPlan_019c420a-15fd-790f-b480-62c38bd7de5e_negatedTerseLabel_en-US" xlink:label="lab_blue_TreasuryStockSharesTransferredToRestrictedStockPlan" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Treasury stock allocated to restricted stock plan, net of forfeitures (in shares)</link:label>
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    <link:label id="lab_us-gaap_PreferredStockSharesIssued_59d2506c-7167-4935-8454-6e5d35b4cfda_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, issued (in shares)</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_3be8f587-dc1f-4180-91a9-6133311be144_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 (used in) provided by operating activities</link:label>
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    <link:label id="lab_us-gaap_TierOneRiskBasedCapital_7128424b-229d-4fdc-a970-6583220709ec_terseLabel_en-US" xlink:label="lab_us-gaap_TierOneRiskBasedCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tier 1 capital</link:label>
    <link:label id="lab_us-gaap_TierOneRiskBasedCapital_label_en-US" xlink:label="lab_us-gaap_TierOneRiskBasedCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Tier 1 Risk-Based Capital, Actual</link:label>
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    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_29a4c9db-2918-4b2b-98c2-a741e333b3c4_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>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_12e95561-adc2-4f5d-bd4e-a096a0572cf1_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>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear_b7e64a0e-4bdf-49fa-8841-40a88fa32784_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan origination, year four</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearFourOriginatedThreeYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Four, Originated, Three Years before Current Fiscal Year</link:label>
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    <link:label id="lab_us-gaap_NumberOfReportableSegments_019b50c9-5ef5-7f6c-8882-578f26c343ac_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"/>
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    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesMaturityRollingYearAbstract_719046a6-3ae7-4d45-8095-ca88bfbe288d_terseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesMaturityRollingYearAbstract" 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_FederalHomeLoanBankAdvancesMaturityRollingYearAbstract_label_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesMaturityRollingYearAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank, Advance, Maturity, Rolling Year [Abstract]</link:label>
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    <link:label id="lab_us-gaap_CommercialRealEstateMember_019b501c-4a1d-7bb7-bd95-f838c282f2a7_verboseLabel_en-US" xlink:label="lab_us-gaap_CommercialRealEstateMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Commercial real estate</link:label>
    <link:label id="lab_us-gaap_CommercialRealEstateMember_ed4e5504-40f0-4eca-bb6c-ec2ffa74c7b7_terseLabel_en-US" xlink:label="lab_us-gaap_CommercialRealEstateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial real estate</link:label>
    <link:label id="lab_us-gaap_CommercialRealEstateMember_label_en-US" xlink:label="lab_us-gaap_CommercialRealEstateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Real Estate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommercialRealEstateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommercialRealEstateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommercialRealEstateMember" xlink:to="lab_us-gaap_CommercialRealEstateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_2a975480-bb72-4df5-ab76-cba1e653309e_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>
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    <link:label id="lab_us-gaap_SubstandardMember_2d7bd423-e4c3-4609-a67a-9a9049944a47_terseLabel_en-US" xlink:label="lab_us-gaap_SubstandardMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Substandard</link:label>
    <link:label id="lab_us-gaap_SubstandardMember_label_en-US" xlink:label="lab_us-gaap_SubstandardMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Substandard [Member]</link:label>
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    <link:label id="lab_us-gaap_InterestAndDividendIncomeOperating_c2a1b44a-0774-46df-8df9-209e3ca70767_totalLabel_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total interest income</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain_69611b13-0d63-44ad-8252-3ac62bd0fe8f_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Asset, Aging [Domain]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Aging [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivablesPeriodPastDueDomain"/>
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    <link:label id="lab_us-gaap_SpecialMentionMember_dbf04800-9157-4a4b-884c-5d0f84924754_terseLabel_en-US" xlink:label="lab_us-gaap_SpecialMentionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Special mention</link:label>
    <link:label id="lab_us-gaap_SpecialMentionMember_label_en-US" xlink:label="lab_us-gaap_SpecialMentionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Special Mention [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SpecialMentionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SpecialMentionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SpecialMentionMember" xlink:to="lab_us-gaap_SpecialMentionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearFour_31f2ee01-040c-4dc8-aa71-e8ccac28b321_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
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    <link:label id="lab_us-gaap_FinancialInstrumentsOwnedAtFairValue_4d683481-3f1c-43db-b6c9-6751bc107cfd_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsOwnedAtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Securities pledged as collateral</link:label>
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    <link:label id="lab_us-gaap_USTreasuryNotesSecuritiesMember_f21b3d24-5442-4a36-a5cc-ac0d70aafb1d_terseLabel_en-US" xlink:label="lab_us-gaap_USTreasuryNotesSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">U.S. Treasury Note</link:label>
    <link:label id="lab_us-gaap_USTreasuryNotesSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_USTreasuryNotesSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Treasury Notes Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USTreasuryNotesSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_USTreasuryNotesSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_USTreasuryNotesSecuritiesMember" xlink:to="lab_us-gaap_USTreasuryNotesSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTable_c4960c4e-7696-4df6-8b0b-d3e31d9eef78_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_PaymentDeferralMember_67a3fa6b-cd9f-427e-bff0-875f0b944575_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentDeferralMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payment Delays</link:label>
    <link:label id="lab_us-gaap_PaymentDeferralMember_label_en-US" xlink:label="lab_us-gaap_PaymentDeferralMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment Deferral [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentDeferralMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentDeferralMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentDeferralMember" xlink:to="lab_us-gaap_PaymentDeferralMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseDeposits_b2075c3f-614e-4cec-893c-94bdac261baa_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseDeposits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deposits</link:label>
    <link:label id="lab_us-gaap_InterestExpenseDeposits_label_en-US" xlink:label="lab_us-gaap_InterestExpenseDeposits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Deposits</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseDeposits" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseDeposits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseDeposits" xlink:to="lab_us-gaap_InterestExpenseDeposits" xlink:type="arc" order="1"/>
    <link:label id="lab_blue_FinancingReceivableAfterAllowanceForCreditLossDeferredFeesCostsAndDiscounts_74f44816-26bc-40d8-9f9c-515eee5185ad_terseLabel_en-US" xlink:label="lab_blue_FinancingReceivableAfterAllowanceForCreditLossDeferredFeesCostsAndDiscounts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans, net of allowance for credit losses</link:label>
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    <link:label id="lab_blue_FinancingReceivableAfterAllowanceForCreditLossDeferredFeesCostsAndDiscounts_documentation_en-US" xlink:label="lab_blue_FinancingReceivableAfterAllowanceForCreditLossDeferredFeesCostsAndDiscounts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, After Allowance For Credit Loss, Deferred Fees, Costs And Discounts</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blue_FinancingReceivableAfterAllowanceForCreditLossDeferredFeesCostsAndDiscounts" xlink:href="blue-20251231.xsd#blue_FinancingReceivableAfterAllowanceForCreditLossDeferredFeesCostsAndDiscounts"/>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_98c1f4ec-6f16-4373-b13f-6781efa763b8_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">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_NoninterestIncomeAbstract_7655abf9-0e5c-4307-ac81-86416c19921e_terseLabel_en-US" xlink:label="lab_us-gaap_NoninterestIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-interest income:</link:label>
    <link:label id="lab_us-gaap_NoninterestIncomeAbstract_label_en-US" xlink:label="lab_us-gaap_NoninterestIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Income [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoninterestIncomeAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoninterestIncomeAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoninterestIncomeAbstract" xlink:to="lab_us-gaap_NoninterestIncomeAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OwnershipDomain_4bd72f31-a1e0-4ac2-ae6b-bb472fa004a9_terseLabel_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:label id="lab_srt_OwnershipDomain_label_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_OwnershipDomain" xlink:to="lab_srt_OwnershipDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_blue_BankOwnedLifeInsurancePolicyPolicyTextBlock_c24eb4aa-6b82-48b6-a470-4756ca40e79e_terseLabel_en-US" xlink:label="lab_blue_BankOwnedLifeInsurancePolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Bank Owned Life Insurance</link:label>
    <link:label id="lab_blue_BankOwnedLifeInsurancePolicyPolicyTextBlock_label_en-US" xlink:label="lab_blue_BankOwnedLifeInsurancePolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Bank Owned Life Insurance, Policy [Policy Text Block]</link:label>
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    <link:label id="lab_blue_ConsumerAndOtherLoansMember_494ef527-f7b5-46e6-96dd-bd2bb886f8df_terseLabel_en-US" xlink:label="lab_blue_ConsumerAndOtherLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consumer and other</link:label>
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    <link:label id="lab_blue_ConsumerAndOtherLoansMember_documentation_en-US" xlink:label="lab_blue_ConsumerAndOtherLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Consumer And Other Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blue_ConsumerAndOtherLoansMember" xlink:href="blue-20251231.xsd#blue_ConsumerAndOtherLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blue_ConsumerAndOtherLoansMember" xlink:to="lab_blue_ConsumerAndOtherLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOwnershipPlanESOPSharesInESOP_c587d736-4f97-4485-9aee-bf8d4c6fadb4_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOwnershipPlanESOPSharesInESOP" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unallocated common stock held by ESOP (in shares)</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOwnershipPlanESOPSharesInESOP_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOwnershipPlanESOPSharesInESOP" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Employee Stock Ownership Plan (ESOP), Shares in ESOP</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOwnershipPlanESOPSharesInESOP" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeStockOwnershipPlanESOPSharesInESOP"/>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearTwo_c16145da-882d-4647-9b15-7dffb4c1c1e9_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearTwo" 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_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearTwo_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Expected Future Benefit Payment, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlanExpectedFutureBenefitPaymentsYearTwo"/>
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    <link:label id="lab_dei_EntityCentralIndexKey_e0805bd8-cc6d-4deb-b29d-6651e671c25f_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>
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    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCentralIndexKey"/>
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    <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"/>
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    <link:label id="lab_us-gaap_Revenues_3bda09c2-85bb-453f-b9aa-1bb2721f0b77_terseLabel_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total income</link:label>
    <link:label id="lab_us-gaap_Revenues_label_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Revenues" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Revenues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Revenues" xlink:to="lab_us-gaap_Revenues" 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>
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    <link:label id="lab_blue_BankingRegulationCapitalConservationBufferAmountTotalRiskBasedCapital_99b91ddc-49e3-4c37-9d06-b2e3502e7d38_terseLabel_en-US" xlink:label="lab_blue_BankingRegulationCapitalConservationBufferAmountTotalRiskBasedCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total capital</link:label>
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    <link:label id="lab_blue_FederalHomeLoanBankAdvanceMaturityFixedInterestRateYearOne_71ae318a-15dd-4967-8288-bb76872eb898_terseLabel_en-US" xlink:label="lab_blue_FederalHomeLoanBankAdvanceMaturityFixedInterestRateYearOne" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025</link:label>
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    <link:label id="lab_blue_FederalHomeLoanBankAdvanceMaturityFixedInterestRateYearOne_documentation_en-US" xlink:label="lab_blue_FederalHomeLoanBankAdvanceMaturityFixedInterestRateYearOne" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank, Advance, Maturity, Fixed Interest Rate, Year One</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock_e165412f-46fb-466f-91a3-f5981340379c_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableCreditQualityIndicatorsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of credit quality indicators</link:label>
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    <link:label id="lab_blue_UnrealizedGainOnDerivatives_10a74c1c-91e2-413e-a359-3268f2f2696a_terseLabel_en-US" xlink:label="lab_blue_UnrealizedGainOnDerivatives" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross unrealized gain included in other assets</link:label>
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    <link:label id="lab_blue_CreditRatingUnspecifiedAaaRatingMember_04002ce2-cbac-40ae-bf18-f3c5a1babc0b_terseLabel_en-US" xlink:label="lab_blue_CreditRatingUnspecifiedAaaRatingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AAA</link:label>
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    <link:label id="lab_blue_CreditRatingUnspecifiedAaaRatingMember_documentation_en-US" xlink:label="lab_blue_CreditRatingUnspecifiedAaaRatingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Credit Rating, Unspecified, Aaa Rating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blue_CreditRatingUnspecifiedAaaRatingMember" xlink:href="blue-20251231.xsd#blue_CreditRatingUnspecifiedAaaRatingMember"/>
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    <link:label id="lab_ecd_AwardExrcPrice_terseLabel_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise Price</link:label>
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    <link:label id="lab_dei_EntityFilerCategory_f4a6ef3f-6d80-4cf3-8092-1ca82d1285c4_terseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
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    <link:label id="lab_us-gaap_TierOneRiskBasedCapitalRequiredForCapitalAdequacyToRiskWeightedAssets_87d40952-09a6-4f0d-acd0-8d16dcdf9d96_terseLabel_en-US" xlink:label="lab_us-gaap_TierOneRiskBasedCapitalRequiredForCapitalAdequacyToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tier 1 capital</link:label>
    <link:label id="lab_us-gaap_TierOneRiskBasedCapitalRequiredForCapitalAdequacyToRiskWeightedAssets_label_en-US" xlink:label="lab_us-gaap_TierOneRiskBasedCapitalRequiredForCapitalAdequacyToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Tier 1 Risk-Based Capital Ratio, Capital Adequacy, Minimum</link:label>
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    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions_25a73a0f-de52-43f3-8ed7-ab84bd8df7d9_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">Expected future expense of non-vested RSUs</link:label>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanBenefitObligationBenefitsPaid_0e981cd0-c1c1-4d4d-913c-c01eed4b1435_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanBenefitObligationBenefitsPaid" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Benefits paid</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember"/>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_25a1f648-163c-4e3a-9867-ce35d39fe068_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss)</link:label>
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    <link:label id="lab_us-gaap_WeightedAverageRateDomesticDepositTimeDeposits_05fb0bea-ef02-4368-8141-e08195d44dd2_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageRateDomesticDepositTimeDeposits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Time deposits</link:label>
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    <link:label id="lab_us-gaap_InternalCreditAssessmentAxis_c06b2c96-d70c-460c-8b3f-bb07b4387169_terseLabel_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Axis]</link:label>
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    <link:label id="lab_us-gaap_InternalCreditAssessmentDomain_label_en-US" xlink:label="lab_us-gaap_InternalCreditAssessmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Internal Credit Assessment [Domain]</link:label>
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    <link:label id="lab_srt_OwnershipAxis_b685a3a0-0f93-4848-bccf-6a99c6b01afc_terseLabel_en-US" xlink:label="lab_srt_OwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Axis]</link:label>
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    <link:label id="lab_blue_ProceedsFromPrincipalPaymentsAndMaturitiesOnSecuritiesHeldToMaturity_019c4210-f50f-7e3d-87e2-327c19d914cb_terseLabel_en-US" xlink:label="lab_blue_ProceedsFromPrincipalPaymentsAndMaturitiesOnSecuritiesHeldToMaturity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principal payments and maturities on securities held to maturity</link:label>
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    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_67969363-ffc1-4091-9771-d12d2c8bb613_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">DERIVATIVES</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_74d3f25a-1ffe-417a-9a95-36f168cc4e98_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">Award Type [Domain]</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_blue_BankingRegulationCapitalConservationBufferAmountCommonEquityTierOneRiskBasedCapital_0b77bd92-5b09-402b-9b0f-c6cfcace032c_terseLabel_en-US" xlink:label="lab_blue_BankingRegulationCapitalConservationBufferAmountCommonEquityTierOneRiskBasedCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common equity tier 1</link:label>
    <link:label id="lab_blue_BankingRegulationCapitalConservationBufferAmountCommonEquityTierOneRiskBasedCapital_label_en-US" xlink:label="lab_blue_BankingRegulationCapitalConservationBufferAmountCommonEquityTierOneRiskBasedCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Capital Conservation Buffer, Amount, Common Equity Tier One Risk-Based Capital</link:label>
    <link:label id="lab_blue_BankingRegulationCapitalConservationBufferAmountCommonEquityTierOneRiskBasedCapital_documentation_en-US" xlink:label="lab_blue_BankingRegulationCapitalConservationBufferAmountCommonEquityTierOneRiskBasedCapital" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Banking Regulation, Capital Conservation Buffer, Amount, Common Equity Tier One Risk-Based Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blue_BankingRegulationCapitalConservationBufferAmountCommonEquityTierOneRiskBasedCapital" xlink:href="blue-20251231.xsd#blue_BankingRegulationCapitalConservationBufferAmountCommonEquityTierOneRiskBasedCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blue_BankingRegulationCapitalConservationBufferAmountCommonEquityTierOneRiskBasedCapital" xlink:to="lab_blue_BankingRegulationCapitalConservationBufferAmountCommonEquityTierOneRiskBasedCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_18db0bc1-73b1-472e-9ded-2ae2a64b3cef_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"/>
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    <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_d1374489-7ed3-440f-b5a8-5f1cd9d2435a_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_44710bc1-0afd-4b78-bfb3-b2dcc5190fae_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</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_cfdf42b5-0160-4b02-bf78-a697f682bea1_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_us-gaap_DefinedBenefitPlanDisclosureLineItems_1240c6d8-57e0-4a6e-be9b-bed45ecaddc8_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan Disclosure [Line Items]</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanDisclosureLineItems_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanDisclosureLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlanDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedBenefitPlanDisclosureLineItems" xlink:to="lab_us-gaap_DefinedBenefitPlanDisclosureLineItems" 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_CapitalRequiredToBeWellCapitalized_a1bafff8-6c2c-40db-882f-368c128b53e8_terseLabel_en-US" xlink:label="lab_us-gaap_CapitalRequiredToBeWellCapitalized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total capital</link:label>
    <link:label id="lab_us-gaap_CapitalRequiredToBeWellCapitalized_label_en-US" xlink:label="lab_us-gaap_CapitalRequiredToBeWellCapitalized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Total Risk-Based Capital, Well Capitalized, Minimum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CapitalRequiredToBeWellCapitalized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalRequiredToBeWellCapitalized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CapitalRequiredToBeWellCapitalized" xlink:to="lab_us-gaap_CapitalRequiredToBeWellCapitalized" xlink:type="arc" order="1"/>
    <link:label id="lab_blue_DeferredTaxAssetsAccruedInterestReceivable_92411563-8e54-470b-9e18-01aa93c7f942_terseLabel_en-US" xlink:label="lab_blue_DeferredTaxAssetsAccruedInterestReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest receivable</link:label>
    <link:label id="lab_blue_DeferredTaxAssetsAccruedInterestReceivable_label_en-US" xlink:label="lab_blue_DeferredTaxAssetsAccruedInterestReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Accrued interest receivable</link:label>
    <link:label id="lab_blue_DeferredTaxAssetsAccruedInterestReceivable_documentation_en-US" xlink:label="lab_blue_DeferredTaxAssetsAccruedInterestReceivable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Accrued interest receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blue_DeferredTaxAssetsAccruedInterestReceivable" xlink:href="blue-20251231.xsd#blue_DeferredTaxAssetsAccruedInterestReceivable"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate_604f999a-ce50-4f65-a0d0-fe647e837649_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">Expected 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"/>
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    <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_RetirementPlanTypeDomain_cf00ba45-dd2e-4d44-89fe-c379cf79181a_terseLabel_en-US" xlink:label="lab_us-gaap_RetirementPlanTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retirement Plan Type [Domain]</link:label>
    <link:label id="lab_us-gaap_RetirementPlanTypeDomain_label_en-US" xlink:label="lab_us-gaap_RetirementPlanTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retirement Plan Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetirementPlanTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RetirementPlanTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetirementPlanTypeDomain" xlink:to="lab_us-gaap_RetirementPlanTypeDomain" 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>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_4866170b-52ac-4d83-a79c-423df1eaa1af_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due from one year to five years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, after Year One Through Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost"/>
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    <link:label id="lab_us-gaap_ScheduleOfAmountsRecognizedInOtherComprehensiveIncomeLossTableTextBlock_26dcd47b-6c1f-48fe-8aec-49e5c6f668af_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAmountsRecognizedInOtherComprehensiveIncomeLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of the amounts recognized in other comprehensive income</link:label>
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    <link:label id="lab_us-gaap_CapitalRequiredForCapitalAdequacy_552585f1-dde2-4423-901a-219b38d41dda_terseLabel_en-US" xlink:label="lab_us-gaap_CapitalRequiredForCapitalAdequacy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total capital</link:label>
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    <link:label id="lab_us-gaap_OperatingLeasePayments_4ae420b1-1dd3-4f42-bde9-e8a8153c04fc_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">Operating cash flows from operating leases</link:label>
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    <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>
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    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_8360738e-a099-4b75-9a1f-5bcb781ccf73_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>
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    <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"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationAwardTrancheTwoMember_05591547-e646-4f4d-970a-cf1e4f45769a_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"/>
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    <link:label id="lab_blue_FinancingReceivableExcludingAccruedInterestIndividuallyEvaluatedForImpairment_e30e9af4-a008-4c86-a157-49f10752026b_terseLabel_en-US" xlink:label="lab_blue_FinancingReceivableExcludingAccruedInterestIndividuallyEvaluatedForImpairment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individually Evaluated</link:label>
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    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_0a1cf5c3-282f-4f9f-9387-4dac8acb468d_verboseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Weighted average shares outstanding-diluted (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_eae8d86a-c275-41f4-9cf6-6e0a48188558_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">Average number of common shares outstanding used to calculate diluted earnings per common share</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"/>
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    <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"/>
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    <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>
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    <link:label id="lab_us-gaap_CurrentFederalStateAndLocalTaxExpenseBenefit_36b67010-41c5-4447-a7ef-bd75171c15de_terseLabel_en-US" xlink:label="lab_us-gaap_CurrentFederalStateAndLocalTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current federal, state and local, tax expense (benefit)</link:label>
    <link:label id="lab_us-gaap_CurrentFederalStateAndLocalTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_CurrentFederalStateAndLocalTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Federal, State and Local, Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CurrentFederalStateAndLocalTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CurrentFederalStateAndLocalTaxExpenseBenefit"/>
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    <link:label id="lab_blue_NonaccrualMember_b8d0335b-92ea-4b03-a77a-1de07893591e_terseLabel_en-US" xlink:label="lab_blue_NonaccrualMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Accrual</link:label>
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    <link:label id="lab_blue_NonaccrualMember_documentation_en-US" xlink:label="lab_blue_NonaccrualMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Nonaccrual</link:label>
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    <link:label id="lab_dei_EntitySmallBusiness_581f9424-cca5-46a1-a783-2595fb5219bb_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>
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    <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>
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    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesNetCarryingAmountAbstract_33426ec0-eca0-426f-8f36-9458d7077b28_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesNetCarryingAmountAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost</link:label>
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    <link:label id="lab_us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTableTextBlock_7ed1a335-883b-457a-ba16-56c041724ec4_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of carrying amounts and fair value of financial instruments not carried at fair value</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTableTextBlock"/>
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    <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>
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    <link:label id="lab_us-gaap_EmployeeStockOwnershipPlanESOPNumberOfAllocatedShares_318fb3e6-2341-4f5b-b947-bc55689f2c18_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOwnershipPlanESOPNumberOfAllocatedShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ESOP shares committed to be released (in shares)</link:label>
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    <link:label id="lab_us-gaap_EquityComponentDomain_2f0d6593-38fd-4663-b8db-42c75274fd87_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>
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    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_34f75294-df16-4b2e-b96b-94ab09ec9705_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"/>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability_ee03a082-de04-4057-b49d-e5af75273a60_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">Change in lease liability</link:label>
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    <link:label id="lab_us-gaap_TreasuryStockAcquiredAverageCostPerShare_3b193851-16a4-40cb-a495-a13b25db0ff2_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockAcquiredAverageCostPerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Average cost per share of shares repurchased (in dollars per share)</link:label>
    <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_dei_DocumentType_4d459967-92d9-4e54-89d8-cf45e47dd9c4_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
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    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_6bd5b659-e402-455f-9eee-8f110eeee737_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Significant Unobservable Inputs</link:label>
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    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_05364b9c-288e-4dca-ae4b-7551fb471bd2_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EARNINGS PER SHARE</link:label>
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    <link:label id="lab_ecd_OutstandingRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" 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_AdditionalPaidInCapital_03e6b17b-c360-4368-8522-6587637dd9af_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:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_1a639369-7080-4f2c-8b6e-3836d8bdf917_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">Total revenue from contracts with customers</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromSaleOfLoansHeldForSale_c20c1e65-bd8c-45fa-8362-43a0576ee944_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sales of loans held for sale</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_c3c6e61f-c32a-426e-a12c-693b304cd97d_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">Total other comprehensive income, net of tax</link:label>
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    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_f9100d93-1aac-49f4-b101-d255c7c8659a_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Quoted Prices in Active Markets for Identical Assets</link:label>
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    <link:label id="lab_us-gaap_RepaymentsOfFederalHomeLoanBankBorrowings_e6fe0ac2-7dc5-4a42-844c-9ea3d4403976_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfFederalHomeLoanBankBorrowings" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repayments of advances from Federal Home Loan Bank</link:label>
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    <link:label id="lab_us-gaap_FederalDepositInsuranceCorporationPremiumExpense_f06de0a3-050d-4cc1-89fb-6e7d22f09b89_terseLabel_en-US" xlink:label="lab_us-gaap_FederalDepositInsuranceCorporationPremiumExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal deposit insurance</link:label>
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    <link:label id="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_aa446516-909f-4f32-aea7-966f2f994e76_terseLabel_en-US" xlink:label="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental noncash disclosures</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract"/>
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    <link:label id="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward_bd9beb11-164d-4a84-b1b7-27e5b8180d3d_terseLabel_en-US" xlink:label="lab_us-gaap_AOCIAttributableToParentNetOfTaxRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent, Net of Tax [Roll Forward]</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod_7af05856-0408-4060-a7cb-1f1398b6ca75_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestModifiedPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans modified in period</link:label>
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    <link:label id="lab_blue_MortgageBackSecuritiesResidentialMember_documentation_en-US" xlink:label="lab_blue_MortgageBackSecuritiesResidentialMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage-Back Securities, Residential</link:label>
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    <link:label id="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_ba4e0efe-cc64-4a7e-8bf7-a7b29138fc67_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares of common stock sold</link:label>
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    <link:label id="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract_label_en-US" xlink:label="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Debt and Equity Securities [Abstract]</link:label>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesContinuousUnrealizedLossPositionFairValueAbstract_1573d2b8-f3ee-4d4d-a9a2-8d17fd602d0f_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesContinuousUnrealizedLossPositionFairValueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-sale, Unrealized Loss Position [Line Items]</link:label>
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    <link:label id="lab_us-gaap_ExtendedMaturityMember_label_en-US" xlink:label="lab_us-gaap_ExtendedMaturityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Extended Maturity [Member]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablePortfolioSegmentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivablePortfolioSegmentAxis"/>
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    <link:loc xlink:type="locator" xlink:label="loc_blue_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOtherCompensationAmount" xlink:href="blue-20251231.xsd#blue_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOtherCompensationAmount"/>
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    <link:label id="lab_us-gaap_ScheduleOfDefinedBenefitPlanAmountsRecognizedInOtherComprehensiveIncomeLossTableTextBlock_9dd0827f-a21a-4ff6-ac41-f524eebeca33_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDefinedBenefitPlanAmountsRecognizedInOtherComprehensiveIncomeLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of amount recognized in accumulated other comprehensive income</link:label>
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    <link:label id="lab_us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock_0eeb984f-8acd-499c-a0c4-660457765f67_terseLabel_en-US" xlink:label="lab_us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES</link:label>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_97a7d753-43b2-4081-9b47-844f83169ff3_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">Long-Lived Tangible Asset [Domain]</link:label>
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    <link:label id="lab_us-gaap_ConsumerPortfolioSegmentMember_019b5053-f6b0-7c37-9492-71b99fc50005_terseLabel_en-US" xlink:label="lab_us-gaap_ConsumerPortfolioSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consumer and other</link:label>
    <link:label id="lab_us-gaap_ConsumerPortfolioSegmentMember_label_en-US" xlink:label="lab_us-gaap_ConsumerPortfolioSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consumer Portfolio Segment [Member]</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_879aaa85-ada4-48e6-ab92-ad48686b9d8c_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>
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    <link:label id="lab_blue_FinancingReceivableExcludingAccruedInterestEvaluatedForImpairment_8523028d-ec20-446f-84c7-9b3cfae253b9_totalLabel_en-US" xlink:label="lab_blue_FinancingReceivableExcludingAccruedInterestEvaluatedForImpairment" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockCommonMember" xlink:to="lab_us-gaap_TreasuryStockCommonMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear_0467c1fe-a2c6-4ae7-9efe-79155b8dde46_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan origination, year one</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year One, Originated, Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearOneOriginatedCurrentFiscalYear" 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_TierOneLeverageCapitalRequiredToBeWellCapitalizedToAverageAssets_50666914-9b1e-4c7f-9603-8cad3c991502_terseLabel_en-US" xlink:label="lab_us-gaap_TierOneLeverageCapitalRequiredToBeWellCapitalizedToAverageAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tier 1 (leverage) capital</link:label>
    <link:label id="lab_us-gaap_TierOneLeverageCapitalRequiredToBeWellCapitalizedToAverageAssets_label_en-US" xlink:label="lab_us-gaap_TierOneLeverageCapitalRequiredToBeWellCapitalizedToAverageAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Tier 1 Leverage Capital Ratio, Well Capitalized, Minimum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TierOneLeverageCapitalRequiredToBeWellCapitalizedToAverageAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TierOneLeverageCapitalRequiredToBeWellCapitalizedToAverageAssets"/>
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    <link:label id="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember_ffe474e9-5518-4e4a-8a6d-8903846997b3_terseLabel_en-US" xlink:label="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">U.S. Government agency obligations</link:label>
    <link:label id="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Government Agencies Debt Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_USGovernmentAgenciesDebtSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:to="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_cdfde21f-9070-4d7d-ba2d-bea75f898e53_verboseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Lease liabilities</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_038e75e6-9f49-46a5-bb12-3e101fe060ae_netLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Total</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_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember_b784f75b-48b5-4162-bd8d-4aab83595404_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">90 Days and Greater Past Due</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Equal to or Greater than 90 Days Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember"/>
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    <link:label id="lab_us-gaap_LiabilitiesAbstract_79246307-4fcc-4f5a-a0cb-1adeabe48110_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" 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_LiabilitiesAbstract_ff608ff6-ec9a-4693-8e59-07bf99799931_verboseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Financial liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAbstract" xlink:to="lab_us-gaap_LiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_blue_ScheduleOfInterestExpenseDomesticDepositsTableTextBlock_c9e86631-d17b-439f-81b3-0ff84f919f1e_terseLabel_en-US" xlink:label="lab_blue_ScheduleOfInterestExpenseDomesticDepositsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of interest expense on deposits</link:label>
    <link:label id="lab_blue_ScheduleOfInterestExpenseDomesticDepositsTableTextBlock_label_en-US" xlink:label="lab_blue_ScheduleOfInterestExpenseDomesticDepositsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule Of Interest Expense, Domestic Deposits [Table Text Block]</link:label>
    <link:label id="lab_blue_ScheduleOfInterestExpenseDomesticDepositsTableTextBlock_documentation_en-US" xlink:label="lab_blue_ScheduleOfInterestExpenseDomesticDepositsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule Of Interest Expense, Domestic Deposits</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blue_ScheduleOfInterestExpenseDomesticDepositsTableTextBlock" xlink:href="blue-20251231.xsd#blue_ScheduleOfInterestExpenseDomesticDepositsTableTextBlock"/>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffAfterRecovery_5a61ec4a-968a-4ed3-ac32-6e39ea1436c2_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffAfterRecovery" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Net charge-offs</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffAfterRecovery_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffAfterRecovery" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Allowance for Credit Loss, Writeoff (Recovery)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffAfterRecovery" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffAfterRecovery"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffAfterRecovery" xlink:to="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossWriteoffAfterRecovery" xlink:type="arc" order="1"/>
    <link:label id="lab_blue_SummaryOfFinancingReceivableTableTextBlock_175f5eaf-b7a0-4383-b95f-255c2badaa90_terseLabel_en-US" xlink:label="lab_blue_SummaryOfFinancingReceivableTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of loans receivable</link:label>
    <link:label id="lab_blue_SummaryOfFinancingReceivableTableTextBlock_label_en-US" xlink:label="lab_blue_SummaryOfFinancingReceivableTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Summary of Financing Receivable [Table Text Block]</link:label>
    <link:label id="lab_blue_SummaryOfFinancingReceivableTableTextBlock_documentation_en-US" xlink:label="lab_blue_SummaryOfFinancingReceivableTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Summary of Financing Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blue_SummaryOfFinancingReceivableTableTextBlock" xlink:href="blue-20251231.xsd#blue_SummaryOfFinancingReceivableTableTextBlock"/>
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    <link:label id="lab_us-gaap_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock_a5ab0f55-9b26-4a9c-adcf-3e00151c4f4d_terseLabel_en-US" xlink:label="lab_us-gaap_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">REGULATORY CAPITAL REQUIREMENTS</link:label>
    <link:label id="lab_us-gaap_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock_label_en-US" xlink:label="lab_us-gaap_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Regulatory Capital Requirements under Banking Regulations [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RegulatoryCapitalRequirementsUnderBankingRegulationsTextBlock"/>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInInterestAndDividendsReceivable_ad00b795-c416-48f4-9bb5-a22c6a9313f2_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInInterestAndDividendsReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Increase in interest and dividends receivable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInInterestAndDividendsReceivable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInInterestAndDividendsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Interest and Dividends Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInInterestAndDividendsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInInterestAndDividendsReceivable"/>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear_d9951d21-0bfb-4c7c-a6ed-990042ffdf3c_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan origination, year three</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Year Three, Originated, Two Years before Current Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestYearThreeOriginatedTwoYearsBeforeCurrentFiscalYear"/>
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    <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"/>
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    <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_DefinedBenefitPlanContributionsByEmployer_164b235c-b93a-40f3-b522-04f624cf7c56_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanContributionsByEmployer" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employer contributions</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanContributionsByEmployer_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanContributionsByEmployer" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Plan Assets, Contributions by Employer</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanContributionsByEmployer" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlanContributionsByEmployer"/>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_c7c08944-f0e8-4850-b9f0-04e1d709e16a_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"/>
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    <link:label id="lab_blue_ConstructionAndLandPortfolioSegmentMember_7ba51060-706b-44d5-b5ae-ad4973022332_terseLabel_en-US" xlink:label="lab_blue_ConstructionAndLandPortfolioSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Construction and Land Portfolio Segment</link:label>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue_e9121d9a-b4d6-497b-bb91-ea36711df2bf_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due in one year or less</link:label>
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    <link:label id="lab_blue_BakersHealthcareGroupLLCBHGMember_019d0925-270e-7666-b3d4-52e848a7aa24_terseLabel_en-US" xlink:label="lab_blue_BakersHealthcareGroupLLCBHGMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Bakers Healthcare Group, LLC (BHG)</link:label>
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    <link:label id="lab_us-gaap_Assets_b5d6e7ed-3fd7-4ca9-bc36-1de2a5a08897_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>
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    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesTextBlock_20d65d48-84a5-44b9-87cf-b0985d287dea_terseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BORROWINGS</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward_2de5e236-c54a-4575-87ab-03724265f6e0_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableAllowanceForCreditLossesRollForward"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_fdad3192-4bb7-4d8b-91ed-e580a7f268bd_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_SegmentReportingOtherItemAmount_label_en-US" xlink:label="lab_us-gaap_SegmentReportingOtherItemAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Other Segment Item, Amount</link:label>
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    <link:label id="lab_us-gaap_InterestExpenseBorrowings_56fe7d25-7087-42c0-ba62-1b05fc36787d_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseBorrowings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Borrowed funds</link:label>
    <link:label id="lab_us-gaap_InterestExpenseBorrowings_label_en-US" xlink:label="lab_us-gaap_InterestExpenseBorrowings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Borrowings</link:label>
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    <link:label id="lab_us-gaap_TimeDepositMaturitiesYearTwo_5bbbcbc1-7000-4d7f-85a2-0b6db99dc59d_terseLabel_en-US" xlink:label="lab_us-gaap_TimeDepositMaturitiesYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
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    <link:label id="lab_us-gaap_CapitalRequiredForCapitalAdequacyToRiskWeightedAssets_815ac737-a7a9-445a-a2b4-2dbbd23d4c6c_terseLabel_en-US" xlink:label="lab_us-gaap_CapitalRequiredForCapitalAdequacyToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total capital</link:label>
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    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesFairValue_019b5010-a70a-7091-8d60-258c2c8e2496_totalLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesFairValue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
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    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_6e1c7a14-2af0-4a6d-ad8a-6aa90ed39e30_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>
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    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_7bffa227-cc8f-4b01-b267-780d5d9e8181_terseLabel_en-US" xlink:label="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease liabilities arising from obtaining right-of-use assets</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffBalanceSheetCreditLossLiabilityCreditLossExpenseReversal" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OffBalanceSheetCreditLossLiabilityCreditLossExpenseReversal"/>
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    <link:label id="lab_srt_ProductsAndServicesDomain_af564e33-03ab-4b8f-bac4-edb14d04e8dd_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_AvailableForSaleSecuritiesAbstract_9a73bd1e-dceb-441b-a5be-e36aaf3f3447_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Available-for-sale</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesAbstract_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_blue_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterestIndividuallyEvaluatedForImpairment_792d720d-9c07-4352-8af1-427b71c06479_terseLabel_en-US" xlink:label="lab_blue_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterestIndividuallyEvaluatedForImpairment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individually Evaluated</link:label>
    <link:label id="lab_blue_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterestIndividuallyEvaluatedForImpairment_label_en-US" xlink:label="lab_blue_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterestIndividuallyEvaluatedForImpairment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss, Excluding Accrued Interest, Individually Evaluated For Impairment</link:label>
    <link:label id="lab_blue_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterestIndividuallyEvaluatedForImpairment_documentation_en-US" xlink:label="lab_blue_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterestIndividuallyEvaluatedForImpairment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss, Excluding Accrued Interest, Individually Evaluated For Impairment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blue_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterestIndividuallyEvaluatedForImpairment" xlink:href="blue-20251231.xsd#blue_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterestIndividuallyEvaluatedForImpairment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blue_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterestIndividuallyEvaluatedForImpairment" xlink:to="lab_blue_FinancingReceivableAllowanceForCreditLossExcludingAccruedInterestIndividuallyEvaluatedForImpairment" xlink:type="arc" order="1"/>
    <link:label id="lab_blue_DebtSecuritiesMortgageAndAssetBackSecuritiesMaturityTerm_d670eeaf-276c-4912-820b-a8bf813c8eef_terseLabel_en-US" xlink:label="lab_blue_DebtSecuritiesMortgageAndAssetBackSecuritiesMaturityTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Term of mortgage and asset backed securities, maturity (exceeds)</link:label>
    <link:label id="lab_blue_DebtSecuritiesMortgageAndAssetBackSecuritiesMaturityTerm_label_en-US" xlink:label="lab_blue_DebtSecuritiesMortgageAndAssetBackSecuritiesMaturityTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Mortgage And Asset Back Securities, Maturity Term</link:label>
    <link:label id="lab_blue_DebtSecuritiesMortgageAndAssetBackSecuritiesMaturityTerm_documentation_en-US" xlink:label="lab_blue_DebtSecuritiesMortgageAndAssetBackSecuritiesMaturityTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Mortgage And Asset Back Securities, Maturity Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blue_DebtSecuritiesMortgageAndAssetBackSecuritiesMaturityTerm" xlink:href="blue-20251231.xsd#blue_DebtSecuritiesMortgageAndAssetBackSecuritiesMaturityTerm"/>
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    <link:label id="lab_us-gaap_PaymentsToAcquireFederalHomeLoanBankStock_4d239f37-83e2-44b3-b61a-8ede533c35ce_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireFederalHomeLoanBankStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of Federal Home Loan Bank stock</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireFederalHomeLoanBankStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireFederalHomeLoanBankStock"/>
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    <link:label id="lab_us-gaap_ProfitLoss_019b50ce-fde3-7056-85e8-1a61caff6f12_verboseLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Loss before undistributed earnings of subsidiary</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_label_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProfitLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProfitLoss" xlink:to="lab_us-gaap_ProfitLoss" 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>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RestatementDoesNotRequireRecoveryTextBlock"/>
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    <link:label id="lab_us-gaap_DerivativeNotionalAmount_837ea9a0-4d32-4f8a-94ab-6e41b800de27_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate swaps, notional amount</link:label>
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    <link:label id="lab_us-gaap_DerivativeNotionalAmount_label_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Notional Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeNotionalAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeNotionalAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeNotionalAmount" xlink:to="lab_us-gaap_DerivativeNotionalAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_blue_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOtherCompensationPercent_019cd8cb-39c0-7d64-bd7c-6bf179707f13_negatedTerseLabel_en-US" xlink:label="lab_blue_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOtherCompensationPercent" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Non-deductible compensation</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_blue_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOtherCompensationPercent" xlink:href="blue-20251231.xsd#blue_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOtherCompensationPercent"/>
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    <link:label id="lab_us-gaap_IncomeTaxReconciliationTaxExemptIncome_59be557b-0fe4-4975-aad4-90f384b0812f_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationTaxExemptIncome" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Tax-exempt income</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationTaxExemptIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationTaxExemptIncome"/>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving_fed780f8-3601-4394-bff7-eb12ebe19576_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revolving Loans</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestRevolving" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestRevolving"/>
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    <link:label id="lab_blue_EmployeeStockOwnershipPlanESOPLoanReceivable_e0c234ac-8aa2-49ca-9bf7-a6e5b85d20dc_terseLabel_en-US" xlink:label="lab_blue_EmployeeStockOwnershipPlanESOPLoanReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ESOP loan receivable</link:label>
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    <link:label id="lab_blue_EmployeeStockOwnershipPlanESOPLoanReceivable_documentation_en-US" xlink:label="lab_blue_EmployeeStockOwnershipPlanESOPLoanReceivable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Employee Stock Ownership Plan (ESOP), Loan Receivable</link:label>
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    <link:label id="lab_dei_CityAreaCode_d4aa2862-f34b-4943-88e3-cc446ac58da1_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>
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    <link:label id="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock_20c65b17-6dc0-465e-ab84-f834b5c057b2_terseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of changes in allowance for loan losses by class of loans</link:label>
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    <link:label id="lab_us-gaap_MortgagesMember_1537c132-3daf-4a2a-bc4c-4823c5bf283f_terseLabel_en-US" xlink:label="lab_us-gaap_MortgagesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgages</link:label>
    <link:label id="lab_us-gaap_MortgagesMember_label_en-US" xlink:label="lab_us-gaap_MortgagesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgages [Member]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_blue_DeferredTaxAssetsCharitableContributionCarryforwardsTerm" xlink:href="blue-20251231.xsd#blue_DeferredTaxAssetsCharitableContributionCarryforwardsTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blue_DeferredTaxAssetsCharitableContributionCarryforwardsTerm" xlink:to="lab_blue_DeferredTaxAssetsCharitableContributionCarryforwardsTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_dd27f4d2-0545-4f6c-9f8c-6bdc68a9461a_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"/>
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    <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"/>
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    <link:label id="lab_us-gaap_ScheduleOfStockOptionsRollForwardTableTextBlock_7264d6f2-0b18-46e4-9b23-6140d655bb32_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockOptionsRollForwardTableTextBlock" 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_ScheduleOfStockOptionsRollForwardTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfStockOptionsRollForwardTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Stock Options Roll Forward [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockOptionsRollForwardTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfStockOptionsRollForwardTableTextBlock"/>
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    <link:label id="lab_us-gaap_FederalIncomeTaxExpenseBenefitContinuingOperationsAbstract_019cde8d-fe98-795f-bc57-5f8fc633217e_terseLabel_en-US" xlink:label="lab_us-gaap_FederalIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (decrease) in federal income tax expense resulting from:</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FederalIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FederalIncomeTaxExpenseBenefitContinuingOperationsAbstract"/>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanAmortizationOfGainsLosses_a0daf270-02a6-4d90-a6e0-52e5969f572a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanAmortizationOfGainsLosses" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net loss (gain)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanAmortizationOfGainsLosses" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlanAmortizationOfGainsLosses"/>
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    <link:label id="lab_blue_OverdraftProtectionCreditLinesMember_f84c6cf4-8d9a-47ef-9cc9-c0ba0954b8e1_terseLabel_en-US" xlink:label="lab_blue_OverdraftProtectionCreditLinesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Overdraft protection credit lines</link:label>
    <link:label id="lab_blue_OverdraftProtectionCreditLinesMember_label_en-US" xlink:label="lab_blue_OverdraftProtectionCreditLinesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Overdraft Protection Credit Lines [Member]</link:label>
    <link:label id="lab_blue_OverdraftProtectionCreditLinesMember_documentation_en-US" xlink:label="lab_blue_OverdraftProtectionCreditLinesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Overdraft Protection Credit Lines</link:label>
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    <link:label id="lab_us-gaap_LeaseCost_59fbada1-76c9-4973-80a5-9e303d2562e5_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 lease cost included as a component of occupancy and equipment</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_CashFlowHedgingMember_0eace64d-ea62-4cf2-a06f-4034aa0ac15e_terseLabel_en-US" xlink:label="lab_us-gaap_CashFlowHedgingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash Flow Hedging</link:label>
    <link:label id="lab_us-gaap_CashFlowHedgingMember_label_en-US" xlink:label="lab_us-gaap_CashFlowHedgingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Flow Hedging [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashFlowHedgingMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashFlowHedgingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashFlowHedgingMember" xlink:to="lab_us-gaap_CashFlowHedgingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilities_3dcb3488-8bba-407b-8662-9f9dbb8b9c7e_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilities_label_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilities" xlink:to="lab_us-gaap_OtherLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseCostTableTextBlock_8df3a189-9e68-41d6-ba2c-f79434107db8_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">Summary of lease cost</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_GainLossOnInvestments_eb2d3a8f-369b-4e18-bffa-d8f5eca27b83_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase in net asset value</link:label>
    <link:label id="lab_us-gaap_GainLossOnInvestments_label_en-US" xlink:label="lab_us-gaap_GainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnInvestments" xlink:to="lab_us-gaap_GainLossOnInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_blue_ServiceChargesOnDepositsMember_f64d829d-05d3-4507-bea2-fe5223e9993a_terseLabel_en-US" xlink:label="lab_blue_ServiceChargesOnDepositsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Service charges on deposits</link:label>
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    <link:label id="lab_blue_ServiceChargesOnDepositsMember_documentation_en-US" xlink:label="lab_blue_ServiceChargesOnDepositsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Service Charges On Deposits</link:label>
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    <link:label id="lab_blue_PerformanceStandbyLettersOfCreditMember_660853e2-668c-47dd-b2a6-7b8ad43bcd58_terseLabel_en-US" xlink:label="lab_blue_PerformanceStandbyLettersOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Performance standby letters of credit</link:label>
    <link:label id="lab_blue_PerformanceStandbyLettersOfCreditMember_label_en-US" xlink:label="lab_blue_PerformanceStandbyLettersOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Performance Standby Letters Of Credit [Member]</link:label>
    <link:label id="lab_blue_PerformanceStandbyLettersOfCreditMember_documentation_en-US" xlink:label="lab_blue_PerformanceStandbyLettersOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Performance Standby Letters Of Credit</link:label>
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    <link:label id="lab_dei_AuditorName_a8a09e34-fdd6-4cf7-9e18-5e1e03c93c64_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>
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    <link:loc xlink:type="locator" xlink:label="loc_dei_AuditorName" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AuditorName"/>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationShareBasedCompensationExcessTaxBenefitAmount_019c74e6-0825-79f6-888c-2395fc9582d7_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationShareBasedCompensationExcessTaxBenefitAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock compensation</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationShareBasedCompensationExcessTaxBenefitAmount_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationShareBasedCompensationExcessTaxBenefitAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Tax Expense (Benefit), Share-Based Payment Arrangement, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationShareBasedCompensationExcessTaxBenefitAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationShareBasedCompensationExcessTaxBenefitAmount"/>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate_cee2bc67-6099-4a0a-a60e-2d6ed618cdca_totalLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Available-for-sale, fair value</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Maturity, Allocated and Single Maturity Date, Fair Value</link:label>
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    <link:label id="lab_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate_229f0265-22a0-477b-ba23-72c2d62104e7_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net gain on sale of real estate owned</link:label>
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    <link:label id="lab_blue_EmployeeStockOwnershipPlanESOPAndShareBasedPaymentArrangementExpense_79ad5352-de4f-46a5-a510-8c8bf6c1aee5_terseLabel_en-US" xlink:label="lab_blue_EmployeeStockOwnershipPlanESOPAndShareBasedPaymentArrangementExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ESOP and stock-based compensation expense</link:label>
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    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_bce2061d-3fef-494a-8c98-06eaf35d7a51_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">Cash paid during the period for:</link:label>
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    <link:label id="lab_us-gaap_OperatingLossCarryforwardsValuationAllowance_a89dc14d-7728-4c73-beaa-66700b073f1d_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwardsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation allowance related to NOL carryforwards</link:label>
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    <link:label id="lab_us-gaap_MarketableSecuritiesPolicy_b862b00e-50c3-4e0c-ba73-78a5a8e5b357_terseLabel_en-US" xlink:label="lab_us-gaap_MarketableSecuritiesPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Securities</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract_019c427a-676b-72b3-9edd-7b03f1a75141_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>
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    <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"/>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanAdditionalInformationAbstract_abfb00c6-bb4c-4018-b849-85737bc4d609_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanAdditionalInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization:</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanAdditionalInformationAbstract_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanAdditionalInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Additional Information [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanAdditionalInformationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlanAdditionalInformationAbstract"/>
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    <link:label id="lab_srt_StockRepurchaseProgramNumberOfSharesAuthorizedToBeRepurchased_06bf501c-4b63-46a8-aa45-86280947f694_terseLabel_en-US" xlink:label="lab_srt_StockRepurchaseProgramNumberOfSharesAuthorizedToBeRepurchased" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of shares authorized for repurchase (in shares)</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableUnamortizedLoanFeeCost_948d08bd-e2b3-4430-af2e-3050b1786ffc_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableUnamortizedLoanFeeCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net deferred loan fees</link:label>
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    <link:label id="lab_us-gaap_LesseeLeasesPolicyTextBlock_e49a4409-d8e0-448c-b1fe-96d2e0c9707f_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 and Lease Obligations</link:label>
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    <link:label id="lab_blue_NonTaxableInvestmentIncome_49d4edd1-b165-4dd9-92ea-4a12fcb5d6cb_terseLabel_en-US" xlink:label="lab_blue_NonTaxableInvestmentIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-taxable investment income</link:label>
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    <link:label id="lab_blue_DeferredTaxAssetFinanceLeaseLiability_c83f0697-99d1-4398-8927-4452a7ace6fb_terseLabel_en-US" xlink:label="lab_blue_DeferredTaxAssetFinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance lease liability</link:label>
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    <link:label id="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction_064a8d77-8985-4fe9-8ea7-bdada65e52f3_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">Gross offering proceeds</link:label>
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    <link:label id="lab_us-gaap_ResidentialMortgageBackedSecuritiesMember_92bc1bf8-daf4-464a-8bf9-10fa11a6eb1d_terseLabel_en-US" xlink:label="lab_us-gaap_ResidentialMortgageBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage-backed securities:</link:label>
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    <link:label id="lab_us-gaap_CapitalRequiredToBeWellCapitalizedToRiskWeightedAssets_8c6514ca-7e1a-4ac3-aea1-499a2f200211_terseLabel_en-US" xlink:label="lab_us-gaap_CapitalRequiredToBeWellCapitalizedToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total capital</link:label>
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    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationAggregateDisclosuresAbstract_4906d544-d322-4acd-b5f9-c862189a8ac4_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationAggregateDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average Remaining Contractual Life (years)</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_04f8866b-3489-4090-872d-11585893bbe9_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">Granted (in dollars per share)</link:label>
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    <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"/>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanInterestCost_f90fcaa4-286d-406e-8ab2-17c804b1caa4_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanInterestCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest cost</link:label>
    <link:label id="lab_us-gaap_DefinedBenefitPlanInterestCost_label_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanInterestCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Benefit Plan, Interest Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedBenefitPlanInterestCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedBenefitPlanInterestCost"/>
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    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThanTwelveMonthsFairValue_31fa4db4-93d9-46fb-b956-8dacd66145b8_terseLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThanTwelveMonthsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less than 12 Months</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThanTwelveMonthsFairValue_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesContinuousUnrealizedLossPositionLessThanTwelveMonthsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Continuous Unrealized Loss Position, Less than 12 Months, Fair Value</link:label>
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    <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>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_fa2cfce4-2bd8-4783-be7d-d1800c34d51c_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Table]</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock_f561fc5a-17a6-4c4f-979d-e38f467ad087_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of interest-rate swaps designated as cash flow hedges</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock"/>
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    <link:label id="lab_us-gaap_TimeDepositLiabilityAboveUsInsuranceLimit_460cf921-7cfc-4c08-a42e-24e3f1e2e709_terseLabel_en-US" xlink:label="lab_us-gaap_TimeDepositLiabilityAboveUsInsuranceLimit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Time deposits that meet or exceed the FDIC insurance limit</link:label>
    <link:label id="lab_us-gaap_TimeDepositLiabilityAboveUsInsuranceLimit_label_en-US" xlink:label="lab_us-gaap_TimeDepositLiabilityAboveUsInsuranceLimit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Time Deposit Liability, above US Insurance Limit</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TimeDepositLiabilityAboveUsInsuranceLimit" xlink:to="lab_us-gaap_TimeDepositLiabilityAboveUsInsuranceLimit" 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>
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    <link:label id="lab_blue_SERPAndDRPMember_e4922125-844f-4f2e-9d0c-a7920bb04508_terseLabel_en-US" xlink:label="lab_blue_SERPAndDRPMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SERP and DRP</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_blue_SERPAndDRPMember" xlink:href="blue-20251231.xsd#blue_SERPAndDRPMember"/>
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    <link:label id="lab_blue_BankingRegulationTierOneRiskBasedCapitalClassificationAsWellCapitalizedRatioAbstract_628f6037-0370-49a0-8987-6d98d65c9131_terseLabel_en-US" xlink:label="lab_blue_BankingRegulationTierOneRiskBasedCapitalClassificationAsWellCapitalizedRatioAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ratio</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossAbstract_778554df-fa35-443a-83f0-f27455392969_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for Credit Losses on Loans</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossAbstract_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAllowanceForCreditLossAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, Allowance for Credit Loss [Abstract]</link:label>
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    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_b324fe88-cc13-44f8-976f-81b086e7f89d_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Comprehensive loss:</link:label>
    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Comprehensive Income [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract"/>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsPropertyPlantAndEquipment_7864d5fb-9297-4306-bc19-2a737eb94bbf_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Premises and equipment</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsPropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Property, Plant and Equipment</link:label>
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    <link:label id="lab_blue_EmployeeStockOwnershipPlanESOPPurchaseOfCommonShares_78531cb6-04b3-4bf8-9114-3cb59dcffe9e_terseLabel_en-US" xlink:label="lab_blue_EmployeeStockOwnershipPlanESOPPurchaseOfCommonShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares purchased for ESOP</link:label>
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    <link:label id="lab_blue_EmployeeStockOwnershipPlanESOPPurchaseOfCommonShares_documentation_en-US" xlink:label="lab_blue_EmployeeStockOwnershipPlanESOPPurchaseOfCommonShares" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Employee Stock Ownership Plan (ESOP), Purchase of Common Shares</link:label>
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    <link:label id="lab_srt_ShareRepurchaseProgramAxis_a2d2c55d-862e-4a42-91fc-1cc045e2eb0a_terseLabel_en-US" xlink:label="lab_srt_ShareRepurchaseProgramAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share Repurchase Program [Axis]</link:label>
    <link:label id="lab_srt_ShareRepurchaseProgramAxis_label_en-US" xlink:label="lab_srt_ShareRepurchaseProgramAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Program [Axis]</link:label>
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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_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_a1fe3b7f-9499-4a3e-8b8a-7f76bce20640_periodStartLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Outstanding, beginning balance (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_9df429f9-bf27-4a5c-bc01-3f371d327624_periodEndLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Outstanding, ending balance (in dollars per share)</link:label>
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    <link:label id="lab_us-gaap_MortgageLoansInProcessOfForeclosureAmount_361c074d-09fb-4117-a668-1ecb927ba117_terseLabel_en-US" xlink:label="lab_us-gaap_MortgageLoansInProcessOfForeclosureAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage loans in process of foreclosure</link:label>
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    <link:label id="lab_blue_ConstructionLineOfCreditMember_70bda11f-638e-43a1-a724-fc650f1ca181_terseLabel_en-US" xlink:label="lab_blue_ConstructionLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Undisbursed construction credit lines</link:label>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue_6145f62b-b0b0-447b-b148-3209ef04c1ce_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after ten years</link:label>
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    <link:label id="lab_us-gaap_PaymentsToAcquireMortgageNotesReceivable_47cbd28b-09d5-487c-b2d5-df51eefb715e_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireMortgageNotesReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of mortgage and consumer loans</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivables60To89DaysPastDueMember_1cc4cf6f-21ca-4476-936d-421330e4311e_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivables60To89DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">60-89 Days Past Due</link:label>
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    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerAbstract_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer [Abstract]</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal_019b5039-4468-7569-a6c4-f1cf8223a98c_verboseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">(Recovery of) provision for credit loss on loans</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableExcludingAccruedInterestCreditLossExpenseReversal"/>
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    <link:label id="lab_us-gaap_LesseeLeaseDescriptionTable_62a6093d-46b0-4e59-b541-c9d695d4f5b9_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"/>
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    <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>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_2807ff7b-7419-4e20-958f-5e9f6d15086f_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>
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    <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"/>
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    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByParent_f5e6402e-51ab-45bd-9ddd-67a38d481e25_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership interest percentage</link:label>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByParent_label_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary, Ownership Percentage, Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestOwnershipPercentageByParent"/>
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    <link:label id="lab_us-gaap_EmployeeStockOwnershipPlanESOPNumberOfSuspenseShares_58eb073d-7eda-4546-b1c6-37a4602d5085_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOwnershipPlanESOPNumberOfSuspenseShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unallocated shares (in shares)</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems_0e4a2fb4-b5d1-4090-8dde-183e6c6a2f92_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Allowance for Credit Loss [Line Items]</link:label>
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    <link:label id="lab_us-gaap_TreasuryStockSharesAcquired_1d996369-1a1d-41d5-8b6e-066fd9d6e263_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockSharesAcquired" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchase of Treasury stock (in shares)</link:label>
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    <link:label id="lab_us-gaap_TreasuryStockSharesAcquired_label_en-US" xlink:label="lab_us-gaap_TreasuryStockSharesAcquired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Shares, Acquired</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice_2da3e250-b995-470a-b097-746736e78794_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>
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    <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>
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    <link:label id="lab_us-gaap_OperatingLossCarryforwardsLineItems_aeb24758-e25b-407d-8285-d3994af4e6cd_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwardsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Loss Carryforwards [Line Items]</link:label>
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    <link:label id="lab_us-gaap_DefinedBenefitPlanServiceCost_b80d144f-02d5-4779-b88a-bcbf974ea901_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedBenefitPlanServiceCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Service cost</link:label>
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    <link:label id="lab_blue_FinancingReceivablePurchasedLoansPrecentPurchased_019c4273-0067-760b-a73b-d1c96e72e031_terseLabel_en-US" xlink:label="lab_blue_FinancingReceivablePurchasedLoansPrecentPurchased" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing receivable, purchased loans, precent purchased</link:label>
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    <link:label id="lab_us-gaap_FairValueMeasurementFrequencyDomain_013bddc9-812d-485d-81c3-c2a0a4f3c14c_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementFrequencyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementFrequencyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementFrequencyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementFrequencyDomain" xlink:to="lab_us-gaap_FairValueMeasurementFrequencyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FederalHomeLoanBanksAbstract_label_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBanksAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Home Loan Banks [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FederalHomeLoanBanksAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FederalHomeLoanBanksAbstract"/>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseRenewalTerm_0dc0703f-8547-4eb5-bdf7-8bcbbb02a9b6_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">Renewal or option to extend term (up to)</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>
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    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_0d062119-cb14-448f-baa0-085e05fbe3b8_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">STOCK TRANSACTIONS</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_LoanRestructuringModificationDomain_e2fe0ab1-eeba-48d3-a723-ae699ae99731_terseLabel_en-US" xlink:label="lab_us-gaap_LoanRestructuringModificationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan Restructuring Modification [Domain]</link:label>
    <link:label id="lab_us-gaap_LoanRestructuringModificationDomain_label_en-US" xlink:label="lab_us-gaap_LoanRestructuringModificationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan Restructuring Modification [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoanRestructuringModificationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoanRestructuringModificationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoanRestructuringModificationDomain" xlink:to="lab_us-gaap_LoanRestructuringModificationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss_af449a7c-26f0-4331-a6af-5d71d8967d6e_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans receivable, net of allowance for credit losses of $14,392 at December&#160;31, 2025 and $12,965 at December&#160;31, 2024</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss_103ed507-951e-4a46-9270-b26283537f8e_totalLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Loans receivable, net</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableExcludingAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Excluding Accrued Interest, after Allowance for Credit Loss</link:label>
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    <link:label id="lab_blue_InterchangeIncomeMember_6680294f-7ac7-4e82-a867-82b6867f62ee_terseLabel_en-US" xlink:label="lab_blue_InterchangeIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interchange income</link:label>
    <link:label id="lab_blue_InterchangeIncomeMember_label_en-US" xlink:label="lab_blue_InterchangeIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interchange Income [Member]</link:label>
    <link:label id="lab_blue_InterchangeIncomeMember_documentation_en-US" xlink:label="lab_blue_InterchangeIncomeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interchange Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blue_InterchangeIncomeMember" xlink:href="blue-20251231.xsd#blue_InterchangeIncomeMember"/>
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    <link:label id="lab_us-gaap_NetIncomeLoss_5831b448-b944-41b4-bb79-de58ae8b6d5a_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 loss</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_576e2939-ca39-4c37-b806-6ed4e4910a8a_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net loss</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_71cf09ca-f4b4-4023-9af4-1d742fbac63a_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">Total reclassification for the period, net of tax</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_31faa4c0-b71c-48da-9042-a7a5111cd1c1_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 loss applicable to common shares</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_SubsequentEventTable_97fed6b9-9daf-4c27-9e9e-0e324b0e6309_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTable_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTable" xlink:to="lab_us-gaap_SubsequentEventTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CapitalToRiskWeightedAssets_612a8aef-1dcc-455b-9905-41297969e7f3_terseLabel_en-US" xlink:label="lab_us-gaap_CapitalToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total capital</link:label>
    <link:label id="lab_us-gaap_CapitalToRiskWeightedAssets_label_en-US" xlink:label="lab_us-gaap_CapitalToRiskWeightedAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Total Risk-Based Capital Ratio, Actual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CapitalToRiskWeightedAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalToRiskWeightedAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CapitalToRiskWeightedAssets" xlink:to="lab_us-gaap_CapitalToRiskWeightedAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConstructionInProgressMember_a80e16a6-7928-4a03-9061-68202e2b3f71_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_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_ed7e609e-ac9e-4948-af70-ec81847f1329_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"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_c5050054-64a3-45a7-96e8-669234b87522_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 service period (in years)</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>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments_019c9f99-cb42-7f4e-a5ef-7d73a12cf07b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other adjustments</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Other Adjustments, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments"/>
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    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_984b15aa-4cae-4697-86c7-409a020de6c5_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting Information [Line Items]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingInformationLineItems"/>
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    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_232b48ae-d4a7-43e0-8e31-eb55622a8476_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockSharesAuthorized"/>
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    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_b57d4adf-ce79-4566-8a45-40d4a00bef0d_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">Purchase of treasury stock</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"/>
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    <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>
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    <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_PriorPeriodReclassificationAdjustmentDescription_c721afae-f97d-4dc3-9ea2-424525b277ab_terseLabel_en-US" xlink:label="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassifications</link:label>
    <link:label id="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription_label_en-US" xlink:label="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification, Comparability Adjustment [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PriorPeriodReclassificationAdjustmentDescription"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:to="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable_9f0162dd-b756-410b-b35b-353214d4774b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Past Due [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFinancingReceivablesPastDueTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:to="lab_us-gaap_ScheduleOfFinancingReceivablesPastDueTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseTermOfContract_108fd236-e371-436e-9cb2-c11e5879950e_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">Operating lease original lease terms (in years)</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_OtherComprehensiveIncomeDerivativesQualifyingAsHedgesBeforeTaxPeriodIncreaseDecreaseAbstract_9cfe5fdb-a7b3-461c-b34e-413226c7ad7c_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeDerivativesQualifyingAsHedgesBeforeTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized gain (loss) on cash flow hedge:</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeDerivativesQualifyingAsHedgesBeforeTaxPeriodIncreaseDecreaseAbstract_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeDerivativesQualifyingAsHedgesBeforeTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), after Reclassification, before Tax [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeDerivativesQualifyingAsHedgesBeforeTaxPeriodIncreaseDecreaseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeDerivativesQualifyingAsHedgesBeforeTaxPeriodIncreaseDecreaseAbstract"/>
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    <link:label id="lab_us-gaap_PaymentsToAcquireRealEstate_019d404c-86d9-7221-afba-e2c8a56d34fa_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireRealEstate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payments to acquire real estate</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireRealEstate_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Real Estate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireRealEstate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireRealEstate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireRealEstate" xlink:to="lab_us-gaap_PaymentsToAcquireRealEstate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestBearingDomesticDepositSavings_019c421b-6a23-7518-b6b9-1c62522f9ff4_terseLabel_en-US" xlink:label="lab_us-gaap_InterestBearingDomesticDepositSavings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Savings</link:label>
    <link:label id="lab_us-gaap_InterestBearingDomesticDepositSavings_label_en-US" xlink:label="lab_us-gaap_InterestBearingDomesticDepositSavings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest-Bearing Domestic Deposit, Savings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestBearingDomesticDepositSavings" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestBearingDomesticDepositSavings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestBearingDomesticDepositSavings" xlink:to="lab_us-gaap_InterestBearingDomesticDepositSavings" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_e10b455b-9ba1-4895-89b5-00887be9d955_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">Retained earnings</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_ResidentialPortfolioSegmentMember_aa09860f-a67c-44e8-8e1b-c64ca0168ba9_terseLabel_en-US" xlink:label="lab_us-gaap_ResidentialPortfolioSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential Portfolio Segment</link:label>
    <link:label id="lab_us-gaap_ResidentialPortfolioSegmentMember_label_en-US" xlink:label="lab_us-gaap_ResidentialPortfolioSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Portfolio Segment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ResidentialPortfolioSegmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ResidentialPortfolioSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ResidentialPortfolioSegmentMember" xlink:to="lab_us-gaap_ResidentialPortfolioSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_blue_PaymentsToAcquirePropertyPlantAndEquipmentNetOfTenantImprovementCredit_019b4f94-9b1c-77e2-9be0-232c18f7842e_negatedTerseLabel_en-US" xlink:label="lab_blue_PaymentsToAcquirePropertyPlantAndEquipmentNetOfTenantImprovementCredit" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of premises and equipment</link:label>
    <link:label id="lab_blue_PaymentsToAcquirePropertyPlantAndEquipmentNetOfTenantImprovementCredit_label_en-US" xlink:label="lab_blue_PaymentsToAcquirePropertyPlantAndEquipmentNetOfTenantImprovementCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments To Acquire Property, Plant, And Equipment, Net Of Tenant Improvement Credit</link:label>
    <link:label id="lab_blue_PaymentsToAcquirePropertyPlantAndEquipmentNetOfTenantImprovementCredit_documentation_en-US" xlink:label="lab_blue_PaymentsToAcquirePropertyPlantAndEquipmentNetOfTenantImprovementCredit" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments To Acquire Property, Plant, And Equipment, Net Of Tenant Improvement Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blue_PaymentsToAcquirePropertyPlantAndEquipmentNetOfTenantImprovementCredit" xlink:href="blue-20251231.xsd#blue_PaymentsToAcquirePropertyPlantAndEquipmentNetOfTenantImprovementCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blue_PaymentsToAcquirePropertyPlantAndEquipmentNetOfTenantImprovementCredit" xlink:to="lab_blue_PaymentsToAcquirePropertyPlantAndEquipmentNetOfTenantImprovementCredit" 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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:to="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:type="arc" order="1"/>
    <link:label id="lab_blue_PublicStockOfferingMember_f6cb8efe-1f37-44f0-91fd-8df9f0d61c18_terseLabel_en-US" xlink:label="lab_blue_PublicStockOfferingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Public stock offering</link:label>
    <link:label id="lab_blue_PublicStockOfferingMember_label_en-US" xlink:label="lab_blue_PublicStockOfferingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Public Stock Offering [Member]</link:label>
    <link:label id="lab_blue_PublicStockOfferingMember_documentation_en-US" xlink:label="lab_blue_PublicStockOfferingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Public Stock Offering</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blue_PublicStockOfferingMember" xlink:href="blue-20251231.xsd#blue_PublicStockOfferingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blue_PublicStockOfferingMember" xlink:to="lab_blue_PublicStockOfferingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOwnershipPlanESOPDeferredSharesFairValue_f9548ddf-c6ac-4ac9-9315-f87cb23e1989_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOwnershipPlanESOPDeferredSharesFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of unallocated shares</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOwnershipPlanESOPDeferredSharesFairValue_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOwnershipPlanESOPDeferredSharesFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Employee Stock Ownership Plan (ESOP), Deferred Shares, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOwnershipPlanESOPDeferredSharesFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeStockOwnershipPlanESOPDeferredSharesFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOwnershipPlanESOPDeferredSharesFairValue" xlink:to="lab_us-gaap_EmployeeStockOwnershipPlanESOPDeferredSharesFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LifeInsuranceCorporateOrBankOwnedChangeInValue_4bb4b198-0265-4922-8429-a9edd3ca0ca0_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_LifeInsuranceCorporateOrBankOwnedChangeInValue" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Increase in BOLI cash surrender value</link:label>
    <link:label id="lab_us-gaap_LifeInsuranceCorporateOrBankOwnedChangeInValue_label_en-US" xlink:label="lab_us-gaap_LifeInsuranceCorporateOrBankOwnedChangeInValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Life Insurance, Corporate or Bank Owned, Change in Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LifeInsuranceCorporateOrBankOwnedChangeInValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LifeInsuranceCorporateOrBankOwnedChangeInValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LifeInsuranceCorporateOrBankOwnedChangeInValue" xlink:to="lab_us-gaap_LifeInsuranceCorporateOrBankOwnedChangeInValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember_11a63fba-68fd-4453-b09b-3893a99139a0_netLabel_en-US" xlink:label="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Unrealized gain on cash flow hedge:</link:label>
    <link:label id="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember_83a9aa97-cddc-48fe-b27c-28ab28839119_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized Gains Cash Flow Hedges</link:label>
    <link:label id="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember_18aeb2b8-1b6f-42e4-a08e-b5849eb9fcdb_verboseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Losses on cash flow hedges:</link:label>
    <link:label id="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Gain (Loss), Net, Cash Flow Hedge, Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember"/>
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    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_019d404d-ca54-716d-9256-90407bccafa6_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeDomain" xlink:to="lab_us-gaap_SubsequentEventTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BankingRegulationCapitalConservationBufferCommonEquityTierOneRiskBasedCapitalActual_191c7ec1-df4f-4e95-880e-02f5d0567c36_terseLabel_en-US" xlink:label="lab_us-gaap_BankingRegulationCapitalConservationBufferCommonEquityTierOneRiskBasedCapitalActual" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common equity tier 1</link:label>
    <link:label id="lab_us-gaap_BankingRegulationCapitalConservationBufferCommonEquityTierOneRiskBasedCapitalActual_label_en-US" xlink:label="lab_us-gaap_BankingRegulationCapitalConservationBufferCommonEquityTierOneRiskBasedCapitalActual" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking Regulation, Capital Conservation Buffer, Common Equity Tier 1 Risk-Based Capital, Actual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BankingRegulationCapitalConservationBufferCommonEquityTierOneRiskBasedCapitalActual" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BankingRegulationCapitalConservationBufferCommonEquityTierOneRiskBasedCapitalActual"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BankingRegulationCapitalConservationBufferCommonEquityTierOneRiskBasedCapitalActual" xlink:to="lab_us-gaap_BankingRegulationCapitalConservationBufferCommonEquityTierOneRiskBasedCapitalActual" 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>
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    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesOther_1e611f70-88c5-4940-a2fe-333998507c7d_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesOther" 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_DeferredTaxLiabilitiesOther_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Other</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilitiesOther" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilitiesOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxLiabilitiesOther" xlink:to="lab_us-gaap_DeferredTaxLiabilitiesOther" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetirementPlanTypeAxis_0e0e1a5a-f5d6-466b-b24d-7e61fcd301a1_terseLabel_en-US" xlink:label="lab_us-gaap_RetirementPlanTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retirement Plan Type [Axis]</link:label>
    <link:label id="lab_us-gaap_RetirementPlanTypeAxis_label_en-US" xlink:label="lab_us-gaap_RetirementPlanTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retirement Plan Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetirementPlanTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RetirementPlanTypeAxis"/>
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    <link:label id="lab_us-gaap_StatementTable_f791f4f5-4a86-4567-93d0-778a34950b54_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_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_a7c5af15-5576-4bc5-a3ac-b297256730b0_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 to net cash (used in) provided by operating activities:</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_0e50bb61-e91d-4fa7-94f8-98fc689e22e0_verboseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Adjustments to reconcile net loss to net cash provided by 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_NetCashProvidedByUsedInFinancingActivitiesAbstract_728c4c3d-1173-43d0-add1-771932b19b57_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" 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_NetCashProvidedByUsedInFinancingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" 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 [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract"/>
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    <link:label id="lab_blue_CreditRatingUnspecifiedAxis_a85ea2be-5700-4c61-8c8e-fe9909b44aab_terseLabel_en-US" xlink:label="lab_blue_CreditRatingUnspecifiedAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Rating, Unspecified [Axis]</link:label>
    <link:label id="lab_blue_CreditRatingUnspecifiedAxis_label_en-US" xlink:label="lab_blue_CreditRatingUnspecifiedAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Rating, Unspecified [Axis]</link:label>
    <link:label id="lab_blue_CreditRatingUnspecifiedAxis_documentation_en-US" xlink:label="lab_blue_CreditRatingUnspecifiedAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Credit Rating, Unspecified</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_blue_CreditRatingUnspecifiedAxis" xlink:href="blue-20251231.xsd#blue_CreditRatingUnspecifiedAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_blue_CreditRatingUnspecifiedAxis" xlink:to="lab_blue_CreditRatingUnspecifiedAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_53a62c00-e2c6-4485-92e4-bb8f2e54e602_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Fiscal Year Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_blue_DeferredTaxAssetsNetOfLiabilitiesBeforeValuationAllowance_019d2590-114a-704e-b733-82bae2ea13d8_totalLabel_en-US" xlink:label="lab_blue_DeferredTaxAssetsNetOfLiabilitiesBeforeValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net deferred tax asset</link:label>
    <link:label id="lab_blue_DeferredTaxAssetsNetOfLiabilitiesBeforeValuationAllowance_label_en-US" xlink:label="lab_blue_DeferredTaxAssetsNetOfLiabilitiesBeforeValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Net Of Liabilities, Before Valuation Allowance</link:label>
    <link:label id="lab_blue_DeferredTaxAssetsNetOfLiabilitiesBeforeValuationAllowance_documentation_en-US" xlink:label="lab_blue_DeferredTaxAssetsNetOfLiabilitiesBeforeValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Net Of Liabilities, Before Valuation Allowance</link:label>
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    <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"/>
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    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValue_059cd501-0904-4377-ad13-ba5b93018d84_totalLabel_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Held-to-maturity, fair value, total</link:label>
    <link:label id="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValue_label_en-US" xlink:label="lab_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Held-to-Maturity, Maturity, Allocated and Single Maturity Date, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValue"/>
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    <link:label id="lab_dei_AmendmentFlag_0abd098f-5125-4425-8edd-b3566d761854_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>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_fda40a43-d9a5-4b3c-b011-23960d0e9ecb_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Estimated Fair Value</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Fair Value, Fiscal Year Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract"/>
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    <link:label id="lab_us-gaap_SaleOfStockPricePerShare_f7b0b42d-6aaf-4644-8ff1-83813f6cc04c_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">Stock price 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_3dc3544c-b7f8-4818-a913-5affb8e1b705_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">Number of shares authorized for grant (in shares)</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromSaleOfRealEstateHeldforinvestment_efc12b39-324a-4434-83d2-b4c2e308d501_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfRealEstateHeldforinvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale of real estate owned</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice_0135115e-451e-4f33-9b81-45f83761c92a_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forfeited (in dollars per share)</link:label>
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    <link:label id="lab_us-gaap_Liabilities_37a9b353-439e-4c97-9d6b-1440e0db92a9_terseLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_label_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Liabilities" xlink:to="lab_us-gaap_Liabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis_05d995af-0fc8-4924-b6d8-086302c0deea_totalLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Available-for-sale, amortized cost, total</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis"/>
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    <link:label id="lab_us-gaap_PaymentsForProceedsFromLoansAndLeases_label_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromLoansAndLeases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for (Proceeds from) Loans and Leases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForProceedsFromLoansAndLeases" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForProceedsFromLoansAndLeases"/>
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    <link:label id="lab_us-gaap_AssetBackedSecuritiesMember_cb3c92c3-9ab6-465b-a0e0-f4c258343295_terseLabel_en-US" xlink:label="lab_us-gaap_AssetBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset-backed securities</link:label>
    <link:label id="lab_us-gaap_AssetBackedSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_AssetBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset-Backed Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetBackedSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetBackedSecuritiesMember"/>
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    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesWeightedAverageInterestRate_fbc562d0-5568-4d5a-a4d8-5b075182602f_verboseLabel_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Weighted average fixed rate</link:label>
    <link:label id="lab_us-gaap_FederalHomeLoanBankAdvancesWeightedAverageInterestRate_label_en-US" xlink:label="lab_us-gaap_FederalHomeLoanBankAdvancesWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Federal Home Loan Bank, Advances, Weighted Average Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FederalHomeLoanBankAdvancesWeightedAverageInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FederalHomeLoanBankAdvancesWeightedAverageInterestRate"/>
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    <link:label id="lab_srt_CounterpartyNameAxis_019d0924-f78d-79a6-8f6e-7fc85cb8f0ef_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>
    <link:label id="lab_srt_CounterpartyNameAxis_label_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Name [Axis]</link:label>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities_f57da861-aac1-4bdd-a9bb-a630dde88bb3_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Estimated Fair Value</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtSecurities"/>
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