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<!--XBRL document created with Toppan Merrill Bridge  11.4.0.1 -->
<!--Based on XBRL 2.1-->
<!--Created on: 7/21/2026 12:48:10 PM-->
<!--Modified on: 7/21/2026 12:48:10 PM-->
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    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentType" xlink:label="dei_DocumentType" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentRegistrationStatement" xlink:label="dei_DocumentRegistrationStatement" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsCurrentAbstract" xlink:to="us-gaap_AssetsCurrentAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Assets, Current [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CURRENT ASSETS:</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Current assets:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and Cash Equivalents, at Carrying Value</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and cash equivalent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and cash equivalents</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedCashCurrent" xlink:label="us-gaap_RestrictedCashCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RestrictedCashCurrent" xlink:to="us-gaap_RestrictedCashCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RestrictedCashCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Restricted Cash, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RestrictedCashCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Restricted Cash</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsReceivableNetCurrent" xlink:label="us-gaap_AccountsReceivableNetCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableNetCurrent" xlink:to="us-gaap_AccountsReceivableNetCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, after Allowance for Credit Loss, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts receivable, net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts receivable, net</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_BankAcceptanceNotesReceivable" xlink:label="bgm_BankAcceptanceNotesReceivable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_BankAcceptanceNotesReceivable" xlink:to="bgm_BankAcceptanceNotesReceivable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_BankAcceptanceNotesReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amounts due from bank as evidenced by a written promise to pay, due within 1 year (or 1 business cycle).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_BankAcceptanceNotesReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bank Acceptance Notes Receivable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_BankAcceptanceNotesReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bank acceptance notes receivable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bgm_BankAcceptanceNotesReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bank acceptance receivable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InventoryNet" xlink:label="us-gaap_InventoryNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryNet" xlink:to="us-gaap_InventoryNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InventoryNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventory, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InventoryNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventories, net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_InventoryNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total inventory</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Supplies" xlink:label="us-gaap_Supplies" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Supplies" xlink:to="us-gaap_Supplies_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Supplies_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Prepaid Supplies</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_Supplies_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Prepayment to suppliers, net</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_InvestmentInTradingSecurities" xlink:label="bgm_InvestmentInTradingSecurities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_InvestmentInTradingSecurities" xlink:to="bgm_InvestmentInTradingSecurities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_InvestmentInTradingSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of investments in trading securities classified as current.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_InvestmentInTradingSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment In Trading Securities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_InvestmentInTradingSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment in trading securities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssetsCurrent" xlink:label="us-gaap_OtherAssetsCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherAssetsCurrent" xlink:to="us-gaap_OtherAssetsCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherAssetsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Assets, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherAssetsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other current assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_OtherAssetsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total other current assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsCurrent" xlink:label="us-gaap_AssetsCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsCurrent" xlink:to="us-gaap_AssetsCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Assets, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_AssetsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">TOTAL CURRENT ASSETS</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_PropertyAndPlantEquipmentExcludingConstructionInProgressNet" xlink:label="bgm_PropertyAndPlantEquipmentExcludingConstructionInProgressNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_PropertyAndPlantEquipmentExcludingConstructionInProgressNet" xlink:to="bgm_PropertyAndPlantEquipmentExcludingConstructionInProgressNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_PropertyAndPlantEquipmentExcludingConstructionInProgressNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">It represents the value of property plant and equipment excluding construction in progress, net.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_PropertyAndPlantEquipmentExcludingConstructionInProgressNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property and Plant Equipment, Excluding Construction In Progress, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_PropertyAndPlantEquipmentExcludingConstructionInProgressNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property and equipment, net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="bgm_PropertyAndPlantEquipmentExcludingConstructionInProgressNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property and equipment, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConstructionInProgressGross" xlink:label="us-gaap_ConstructionInProgressGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConstructionInProgressGross" xlink:to="us-gaap_ConstructionInProgressGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConstructionInProgressGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Construction in Progress, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConstructionInProgressGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Construction in progress</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:to="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible Assets, Net (Excluding Goodwill)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible assets, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Goodwill" xlink:label="us-gaap_Goodwill" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Goodwill" xlink:to="us-gaap_Goodwill_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Goodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_Goodwill_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermInvestments" xlink:label="us-gaap_LongTermInvestments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermInvestments" xlink:to="us-gaap_LongTermInvestments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-term Investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long term investment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseRightOfUseAsset" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseRightOfUseAsset" xlink:to="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease, Right-of-Use Asset</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating lease right of use assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total operating lease assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxAssetsNet" xlink:label="us-gaap_DeferredIncomeTaxAssetsNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredIncomeTaxAssetsNet" xlink:to="us-gaap_DeferredIncomeTaxAssetsNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredIncomeTaxAssetsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Income Tax Assets, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DeferredIncomeTaxAssetsNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred tax assets</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_PrepaymentsForPropertyAndEquipment" xlink:label="bgm_PrepaymentsForPropertyAndEquipment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_PrepaymentsForPropertyAndEquipment" xlink:to="bgm_PrepaymentsForPropertyAndEquipment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_PrepaymentsForPropertyAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of Prepayments for property and equipment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_PrepaymentsForPropertyAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Prepayment for property and equipment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_PrepaymentsForPropertyAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Prepayments for property and equipment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssetsNoncurrent" xlink:label="us-gaap_OtherAssetsNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherAssetsNoncurrent" xlink:to="us-gaap_OtherAssetsNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Assets, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other long term assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Assets" xlink:label="us-gaap_Assets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Assets" xlink:to="us-gaap_Assets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Assets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_Assets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">TOTAL ASSETS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesCurrentAbstract" xlink:label="us-gaap_LiabilitiesCurrentAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesCurrentAbstract" xlink:to="us-gaap_LiabilitiesCurrentAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities, Current [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">CURRENT LIABILITIES:</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Current liabilities:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansPayableToBankCurrent" xlink:label="us-gaap_LoansPayableToBankCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LoansPayableToBankCurrent" xlink:to="us-gaap_LoansPayableToBankCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LoansPayableToBankCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loans Payable to Bank, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LoansPayableToBankCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bank loans</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccruedInsuranceCurrent" xlink:label="us-gaap_AccruedInsuranceCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccruedInsuranceCurrent" xlink:to="us-gaap_AccruedInsuranceCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccruedInsuranceCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued Insurance, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccruedInsuranceCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Insurance premium payables</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsPayableCurrent" xlink:label="us-gaap_AccountsPayableCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsPayableCurrent" xlink:to="us-gaap_AccountsPayableCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Payable, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractWithCustomerLiabilityCurrent" xlink:label="us-gaap_ContractWithCustomerLiabilityCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ContractWithCustomerLiabilityCurrent" xlink:to="us-gaap_ContractWithCustomerLiabilityCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ContractWithCustomerLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract with Customer, Liability, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ContractWithCustomerLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ContractWithCustomerLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Advance from customers</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_DeferredGovernmentGrantsCurrent" xlink:label="bgm_DeferredGovernmentGrantsCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_DeferredGovernmentGrantsCurrent" xlink:to="bgm_DeferredGovernmentGrantsCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_DeferredGovernmentGrantsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of current deferred government grants.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_DeferredGovernmentGrantsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Government Grants, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_DeferredGovernmentGrantsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred government grants-current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bgm_DeferredGovernmentGrantsCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred government grants - current</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TaxesPayableCurrent" xlink:label="us-gaap_TaxesPayableCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TaxesPayableCurrent" xlink:to="us-gaap_TaxesPayableCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TaxesPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Taxes Payable, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TaxesPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Taxes payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_TaxesPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilityCurrent" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseLiabilityCurrent" xlink:to="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease, Liability, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Current operating lease liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating lease liabilities, current</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLiabilitiesCurrent" xlink:label="us-gaap_OtherLiabilitiesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherLiabilitiesCurrent" xlink:to="us-gaap_OtherLiabilitiesCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Liabilities, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherLiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Due to related party</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLiabilityCurrentRelatedPartyTypeExtensibleEnumeration" xlink:label="us-gaap_OtherLiabilityCurrentRelatedPartyTypeExtensibleEnumeration" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherLiabilityCurrentRelatedPartyTypeExtensibleEnumeration" xlink:to="us-gaap_OtherLiabilityCurrentRelatedPartyTypeExtensibleEnumeration_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherLiabilityCurrentRelatedPartyTypeExtensibleEnumeration_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Liability, Current, Related Party [Extensible Enumeration]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:label="us-gaap_AccruedLiabilitiesAndOtherLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:to="us-gaap_AccruedLiabilitiesAndOtherLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccruedLiabilitiesAndOtherLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued Liabilities and Other Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccruedLiabilitiesAndOtherLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued expenses and other payables</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AccruedLiabilitiesAndOtherLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued expenses and other payables</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesCurrent" xlink:label="us-gaap_LiabilitiesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesCurrent" xlink:to="us-gaap_LiabilitiesCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">TOTAL CURRENT LIABILITIES</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesNoncurrentAbstract" xlink:label="us-gaap_LiabilitiesNoncurrentAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesNoncurrentAbstract" xlink:to="us-gaap_LiabilitiesNoncurrentAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesNoncurrentAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities, Noncurrent [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LiabilitiesNoncurrentAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">LONG TERM LIABILITIES</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:to="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease, Liability, Noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating lease liabilities, noncurrent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-current operating lease liabilities</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_DeferredGovernmentGrantsNonCurrent" xlink:label="bgm_DeferredGovernmentGrantsNonCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_DeferredGovernmentGrantsNonCurrent" xlink:to="bgm_DeferredGovernmentGrantsNonCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_DeferredGovernmentGrantsNonCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of non-current deferred government grants.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_DeferredGovernmentGrantsNonCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Government Grants, Non-Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_DeferredGovernmentGrantsNonCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred government grants - noncurrent</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Liabilities" xlink:label="us-gaap_Liabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_Liabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Liabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_Liabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">TOTAL LIABILITIES</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommitmentsAndContingencies" xlink:label="us-gaap_CommitmentsAndContingencies" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommitmentsAndContingencies" xlink:to="us-gaap_CommitmentsAndContingencies_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commitments and contingencies</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:to="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' Equity, Including Portion Attributable to Noncontrolling Interest [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SHAREHOLDERS' EQUITY:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockValue" xlink:label="us-gaap_CommonStockValue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockValue" xlink:to="us-gaap_CommonStockValue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Value, Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockValue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ordinary Shares, $0.00833335 par value, 5,030,000,000 and 100,000,000 shares authorized, 200,623,358 and 7,226,480 Ordinary Shares, consisting of 180,623,358 and 7,226,480 Class A ordinary shares, par value US$0.00833335 per share, and 20,000,000 Class B ordinary shares, par value US$0.00833335 per share, as of September 30, 2025 and 2024 respectively</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalPaidInCapital" xlink:label="us-gaap_AdditionalPaidInCapital" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional Paid in Capital</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Retained Earnings (Accumulated Deficit)</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:to="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accumulated Other Comprehensive Income (Loss), Net of Tax</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accumulated other comprehensive profit (loss)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquity" xlink:label="us-gaap_StockholdersEquity" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_StockholdersEquity_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' Equity Attributable to Parent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_StockholdersEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total shareholders' equity attributable to BGM Group Ltd.</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterest" xlink:label="us-gaap_MinorityInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MinorityInterest" xlink:to="us-gaap_MinorityInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MinorityInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' Equity Attributable to Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MinorityInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling interests</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:to="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' Equity, Including Portion Attributable to Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Balance as of ending</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Balance as of beginning</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">TOTAL SHAREHOLDERS' EQUITY</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAndStockholdersEquity" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities and Equity</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">TOTAL LIABILITIES AND SHAREHOLDERS' EQUITY</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockParOrStatedValuePerShare" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Par or Stated Value Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ordinary Shares, par value (in dollar per share)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Par value</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesAuthorized" xlink:label="us-gaap_CommonStockSharesAuthorized" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockSharesAuthorized" xlink:to="us-gaap_CommonStockSharesAuthorized_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Shares Authorized</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ordinary Shares, shares authorized</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesIssued" xlink:label="us-gaap_CommonStockSharesIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockSharesIssued" xlink:to="us-gaap_CommonStockSharesIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Shares, Issued</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ordinary Shares, shares issued</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesOutstanding" xlink:label="us-gaap_CommonStockSharesOutstanding" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockSharesOutstanding" xlink:to="us-gaap_CommonStockSharesOutstanding_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Shares, Outstanding</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Balance as of ending (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Balance as of beginning (in shares)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ordinary Shares, shares outstanding</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:label="us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:to="us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consolidated Statements of Operations and Comprehensive Income (Loss)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:to="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue from Contract with Customer, Excluding Assessed Tax</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">NET REVENUE</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CostOfRevenue" xlink:label="us-gaap_CostOfRevenue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CostOfRevenue" xlink:to="us-gaap_CostOfRevenue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CostOfRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cost of Revenue</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CostOfRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">COST OF REVENUE</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CostOfRevenue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cost of revenue</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GrossProfit" xlink:label="us-gaap_GrossProfit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GrossProfit" xlink:to="us-gaap_GrossProfit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GrossProfit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gross Profit</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GrossProfit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gross Profit</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_GrossProfit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">GROSS PROFIT</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SellingGeneralAndAdministrativeExpense" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SellingGeneralAndAdministrativeExpense" xlink:to="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Selling, General and Administrative Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SELLING, GENERAL AND ADMINISTRATIVE</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ResearchAndDevelopmentExpense" xlink:label="us-gaap_ResearchAndDevelopmentExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ResearchAndDevelopmentExpense" xlink:to="us-gaap_ResearchAndDevelopmentExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ResearchAndDevelopmentExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Research and Development Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ResearchAndDevelopmentExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Research and development expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ResearchAndDevelopmentExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">RESEARCH AND DEVELOPMENT EXPENSES</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingIncomeLoss" xlink:label="us-gaap_OperatingIncomeLoss" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingIncomeLoss" xlink:to="us-gaap_OperatingIncomeLoss_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InterestIncomeExpenseNonoperatingNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest income (expense), net</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_InvestmentGainLoss" xlink:label="bgm_InvestmentGainLoss" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_InvestmentGainLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of investment gain (loss).</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_InvestmentGainLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment Gain Loss</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentRealizedGainLossOnDisposal" xlink:label="us-gaap_EquityMethodInvestmentRealizedGainLossOnDisposal" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestmentRealizedGainLossOnDisposal_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment, Realized Gain (Loss) on Disposal</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_EquityMethodInvestmentRealizedGainLossOnDisposal_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on disposal of Long term investment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:label="us-gaap_EquityMethodInvestmentRealizedGainLossOnDisposal_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on disposal of long term investment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EquityMethodInvestmentRealizedGainLossOnDisposal_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loss on disposal of Long term investment</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_InvestmentsInShareOfResultsOfAssociates" xlink:label="bgm_InvestmentsInShareOfResultsOfAssociates" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_InvestmentsInShareOfResultsOfAssociates" xlink:to="bgm_InvestmentsInShareOfResultsOfAssociates_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_InvestmentsInShareOfResultsOfAssociates_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of investments in share of results of associates.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_InvestmentsInShareOfResultsOfAssociates_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investments In Share of Results of Associates</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="bgm_InvestmentsInShareOfResultsOfAssociates_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share of results of associates</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_InvestmentsInShareOfResultsOfAssociates_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share of results of associates</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_GrantIncome" xlink:label="bgm_GrantIncome" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_GrantIncome_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of grant income.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_GrantIncome_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Grant Income</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_GrantIncome_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Grant income</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherNonoperatingIncomeExpense" xlink:label="us-gaap_OtherNonoperatingIncomeExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherNonoperatingIncomeExpense" xlink:to="us-gaap_OtherNonoperatingIncomeExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Nonoperating Income (Expense)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Income (expenses)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NonoperatingIncomeExpense" xlink:label="us-gaap_NonoperatingIncomeExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NonoperatingIncomeExpense" xlink:to="us-gaap_NonoperatingIncomeExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NonoperatingIncomeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Nonoperating Income (Expense)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NonoperatingIncomeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total other expense</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">LOSS BEFORE INCOME TAX PROVISION</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">(loss) Income from operations</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxExpenseBenefit" xlink:label="us-gaap_IncomeTaxExpenseBenefit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="us-gaap_IncomeTaxExpenseBenefit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Tax Expense (Benefit)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">INCOME TAX EXPENSE/(BENEFIT)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProfitLoss" xlink:label="us-gaap_ProfitLoss" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProfitLoss" xlink:to="us-gaap_ProfitLoss_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProfitLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProfitLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net loss</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_ProfitLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">NET LOSS</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ProfitLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net loss for the year</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:label="us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:to="us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Income (Loss) Attributable to Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less: net loss attributable to non-controlling interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLoss" xlink:label="us-gaap_NetIncomeLoss" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_NetIncomeLoss_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetIncomeLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">NET LOSS ATTRIBUTABLE TO BGM Group Ltd.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_NetIncomeLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net (loss) income</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomeNetOfTaxAbstract" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ComprehensiveIncomeNetOfTaxAbstract" xlink:to="us-gaap_ComprehensiveIncomeNetOfTaxAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive Income (Loss), Net of Tax, Attributable to Parent [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">OTHER COMPREHENSIVE LOSS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:to="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Foreign currency translation adjustment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:to="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive Income (Loss), Net of Tax, Including Portion Attributable to Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">COMPREHENSIVE LOSS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:to="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive Income (Loss), Net of Tax, Attributable to Noncontrolling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less: comprehensive loss attributable to non - controlling interests</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomeNetOfTax" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="us-gaap_ComprehensiveIncomeNetOfTax_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">COMPREHENSIVE LOSS ATTRIBUTABLE TO BGM Group Ltd.</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareBasic" xlink:label="us-gaap_EarningsPerShareBasic" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerShareBasic" xlink:to="us-gaap_EarningsPerShareBasic_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Earnings Per Share, Basic</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted average shares - basic (in shares)</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_StatutoryReserveMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Representing member information pertaining to statutory reserve.</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accumulated Other Comprehensive Profit (Loss)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ParentMember" xlink:label="us-gaap_ParentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ParentMember" xlink:to="us-gaap_ParentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ParentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The Shareholders' Equity Attributable to BGM Group Ltd</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Stockholders' Equity [Roll Forward]</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, New Issues</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common shares</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, New Issues</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Issuance of common shares (in shares)</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_StockIssuedDuringPeriodValueStockOptionsGrantedToEmployees" xlink:label="bgm_StockIssuedDuringPeriodValueStockOptionsGrantedToEmployees" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_StockIssuedDuringPeriodValueStockOptionsGrantedToEmployees" xlink:to="bgm_StockIssuedDuringPeriodValueStockOptionsGrantedToEmployees_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_StockIssuedDuringPeriodValueStockOptionsGrantedToEmployees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Value of shares issued during the period to stock options granted to employees.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_StockIssuedDuringPeriodValueStockOptionsGrantedToEmployees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Value, Stock Options Granted to Employees</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_StockIssuedDuringPeriodValueStockOptionsGrantedToEmployees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock options granted to employees</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_StockIssuedDuringPeriodSharesStockOptionsGrantedToEmployees" xlink:label="bgm_StockIssuedDuringPeriodSharesStockOptionsGrantedToEmployees" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_StockIssuedDuringPeriodSharesStockOptionsGrantedToEmployees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares issued during the period to stock options granted to employees.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_StockIssuedDuringPeriodSharesStockOptionsGrantedToEmployees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Issued During Period, Shares, Stock Options Granted to Employees</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_StockIssuedDuringPeriodSharesStockOptionsGrantedToEmployees_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock options granted to employees (in shares)</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_AppropriationsToStatutoryReserve" xlink:label="bgm_AppropriationsToStatutoryReserve" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_AppropriationsToStatutoryReserve_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Appropriations To Statutory Reserve</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DepreciationDepletionAndAmortization" xlink:to="us-gaap_DepreciationDepletionAndAmortization_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensation" xlink:label="us-gaap_ShareBasedCompensation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensation" xlink:to="us-gaap_ShareBasedCompensation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share-Based Payment Arrangement, Noncash Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock based compensation</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProvisionForDoubtfulAccounts" xlink:label="us-gaap_ProvisionForDoubtfulAccounts" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProvisionForDoubtfulAccounts" xlink:to="us-gaap_ProvisionForDoubtfulAccounts_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProvisionForDoubtfulAccounts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, Credit Loss Expense (Reversal)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProvisionForDoubtfulAccounts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Credit loss for accounts receivable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ProvisionForDoubtfulAccounts_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Addition</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProvisionForOtherCreditLosses" xlink:label="us-gaap_ProvisionForOtherCreditLosses" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProvisionForOtherCreditLosses" xlink:to="us-gaap_ProvisionForOtherCreditLosses_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProvisionForOtherCreditLosses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Provision for Other Credit Losses</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProvisionForOtherCreditLosses_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Provision (reverse) for other receivables</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCostAndExpenseOperating" xlink:label="us-gaap_OtherCostAndExpenseOperating" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherCostAndExpenseOperating" xlink:to="us-gaap_OtherCostAndExpenseOperating_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherCostAndExpenseOperating_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Cost and Expense, Operating</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherCostAndExpenseOperating_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Allowance for ATV</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_ImpairmentOfPropertyAndEquipment" xlink:label="bgm_ImpairmentOfPropertyAndEquipment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_ImpairmentOfPropertyAndEquipment" xlink:to="bgm_ImpairmentOfPropertyAndEquipment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_ImpairmentOfPropertyAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aggregate amount of write-off charged during the period for property, plant and equipment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_ImpairmentOfPropertyAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impairment Of Property And Equipment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_ImpairmentOfPropertyAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impairment of property and equipment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InventoryLIFOReserveEffectOnIncomeNet" xlink:label="us-gaap_InventoryLIFOReserveEffectOnIncomeNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryLIFOReserveEffectOnIncomeNet" xlink:to="us-gaap_InventoryLIFOReserveEffectOnIncomeNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InventoryLIFOReserveEffectOnIncomeNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventory, LIFO Reserve, Effect on Income, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InventoryLIFOReserveEffectOnIncomeNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventories provision (reserve)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:to="us-gaap_DeferredIncomeTaxExpenseBenefit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Income Tax Expense (Benefit)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred tax expense (benefit)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MarketableSecuritiesUnrealizedGainLoss" xlink:label="us-gaap_MarketableSecuritiesUnrealizedGainLoss" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MarketableSecuritiesUnrealizedGainLoss" xlink:to="us-gaap_MarketableSecuritiesUnrealizedGainLoss_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MarketableSecuritiesUnrealizedGainLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Marketable Securities, Unrealized Gain (Loss)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_MarketableSecuritiesUnrealizedGainLoss_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unrealized loss from investment in securities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeNet" xlink:label="us-gaap_InvestmentIncomeNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentIncomeNet" xlink:to="us-gaap_InvestmentIncomeNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InvestmentIncomeNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment Income, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_InvestmentIncomeNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment (income)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnDispositionOfAssets1" xlink:label="us-gaap_GainLossOnDispositionOfAssets1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GainLossOnDispositionOfAssets1" xlink:to="us-gaap_GainLossOnDispositionOfAssets1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GainLossOnDispositionOfAssets1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gain (Loss) on Disposition of Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_GainLossOnDispositionOfAssets1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property and equipment written off</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:to="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Operating Capital [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Changes in operating assets and liabilities:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:to="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Accounts Receivable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts receivable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInInsuranceLiabilities" xlink:label="us-gaap_IncreaseDecreaseInInsuranceLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInInsuranceLiabilities" xlink:to="us-gaap_IncreaseDecreaseInInsuranceLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInInsuranceLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Insurance Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInInsuranceLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Insurance premium payables</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_IncreaseDecreaseInBankAcceptanceNotesReceivable" xlink:label="bgm_IncreaseDecreaseInBankAcceptanceNotesReceivable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_IncreaseDecreaseInBankAcceptanceNotesReceivable" xlink:to="bgm_IncreaseDecreaseInBankAcceptanceNotesReceivable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_IncreaseDecreaseInBankAcceptanceNotesReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The increase (decrease) during the reporting period of the amounts due from bank evidenced by a note.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_IncreaseDecreaseInBankAcceptanceNotesReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase Decrease In Bank Acceptance Notes Receivable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="bgm_IncreaseDecreaseInBankAcceptanceNotesReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bank acceptance notes receivable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInInventories" xlink:label="us-gaap_IncreaseDecreaseInInventories" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInInventories" xlink:to="us-gaap_IncreaseDecreaseInInventories_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInInventories_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Inventories</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_IncreaseDecreaseInInventories_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventories</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInPrepaidSupplies" xlink:label="us-gaap_IncreaseDecreaseInPrepaidSupplies" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInPrepaidSupplies_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Prepaid Supplies</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_IncreaseDecreaseInPrepaidSupplies_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Prepayment to suppliers</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOtherCurrentAssets" xlink:label="us-gaap_IncreaseDecreaseInOtherCurrentAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInOtherCurrentAssets" xlink:to="us-gaap_IncreaseDecreaseInOtherCurrentAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInOtherCurrentAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Other Current Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_IncreaseDecreaseInOtherCurrentAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other current assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInAccountsPayableTrade" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayableTrade" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInAccountsPayableTrade" xlink:to="us-gaap_IncreaseDecreaseInAccountsPayableTrade_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayableTrade_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Accounts Payable, Trade</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayableTrade_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:label="us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:to="us-gaap_IncreaseDecreaseInContractWithCustomerLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInContractWithCustomerLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Contract with Customer, Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInContractWithCustomerLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contract liabilities</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_IncreaseDecreaseInDeferredGovernmentGrants" xlink:label="bgm_IncreaseDecreaseInDeferredGovernmentGrants" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_IncreaseDecreaseInDeferredGovernmentGrants" xlink:to="bgm_IncreaseDecreaseInDeferredGovernmentGrants_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_IncreaseDecreaseInDeferredGovernmentGrants_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of increase (decrease) in deferred government grants.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_IncreaseDecreaseInDeferredGovernmentGrants_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Deferred Government Grants</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="bgm_IncreaseDecreaseInDeferredGovernmentGrants_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred government grants</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInAccruedIncomeTaxesPayable" xlink:label="us-gaap_IncreaseDecreaseInAccruedIncomeTaxesPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInAccruedIncomeTaxesPayable" xlink:to="us-gaap_IncreaseDecreaseInAccruedIncomeTaxesPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInAccruedIncomeTaxesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Income Taxes Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInAccruedIncomeTaxesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Taxes payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:to="us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Accrued Liabilities and Other Operating Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accrued expenses and other payables</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_IncreaseDecreaseInOperatingLeaseLiabilities" xlink:label="bgm_IncreaseDecreaseInOperatingLeaseLiabilities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_IncreaseDecreaseInOperatingLeaseLiabilities" xlink:to="bgm_IncreaseDecreaseInOperatingLeaseLiabilities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_IncreaseDecreaseInOperatingLeaseLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The increase (decrease) during the reporting period pertaining to operating lease liabilities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_IncreaseDecreaseInOperatingLeaseLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase (Decrease) in Operating Lease Liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_IncreaseDecreaseInOperatingLeaseLiabilities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lease liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Cash Provided by (Used in) Operating Activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net cash provided by operating activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net cash (used in) provided by operating activities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Cash Provided by (Used in) Investing Activities [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash flows from investing activities:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:to="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to Acquire Property, Plant, and Equipment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase of property and equipment</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_PaymentsForConstructionInProgress" xlink:label="bgm_PaymentsForConstructionInProgress" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_PaymentsForConstructionInProgress" xlink:to="bgm_PaymentsForConstructionInProgress_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_PaymentsForConstructionInProgress_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">It represents the value of payments for construction in progress.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_PaymentsForConstructionInProgress_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments for Construction in Progress</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="bgm_PaymentsForConstructionInProgress_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payment for construction in progress</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireIntangibleAssets" xlink:label="us-gaap_PaymentsToAcquireIntangibleAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquireIntangibleAssets" xlink:to="us-gaap_PaymentsToAcquireIntangibleAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsToAcquireIntangibleAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to Acquire Intangible Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentsToAcquireIntangibleAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase of intangible assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleOfLongtermInvestments" xlink:label="us-gaap_ProceedsFromSaleOfLongtermInvestments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromSaleOfLongtermInvestments" xlink:to="us-gaap_ProceedsFromSaleOfLongtermInvestments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromSaleOfLongtermInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Sale of Long-Term Investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromSaleOfLongtermInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash received from disposal of Long term investment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAcquiredFromAcquisition" xlink:label="us-gaap_CashAcquiredFromAcquisition" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashAcquiredFromAcquisition" xlink:to="us-gaap_CashAcquiredFromAcquisition_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashAcquiredFromAcquisition_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash Acquired from Acquisition</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashAcquiredFromAcquisition_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash received from acquisition</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital" xlink:label="us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital" xlink:to="us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Equity Method Investment, Distribution, Return of Capital</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dividend received</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForProceedsFromShortTermInvestments" xlink:label="us-gaap_PaymentsForProceedsFromShortTermInvestments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsForProceedsFromShortTermInvestments" xlink:to="us-gaap_PaymentsForProceedsFromShortTermInvestments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsForProceedsFromShortTermInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to Acquire Short-Term Investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentsForProceedsFromShortTermInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payment for short term investment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleMaturityAndCollectionOfShorttermInvestments" xlink:label="us-gaap_ProceedsFromSaleMaturityAndCollectionOfShorttermInvestments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromSaleMaturityAndCollectionOfShorttermInvestments" xlink:to="us-gaap_ProceedsFromSaleMaturityAndCollectionOfShorttermInvestments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromSaleMaturityAndCollectionOfShorttermInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Sale, Maturity and Collection of Short-Term Investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromSaleMaturityAndCollectionOfShorttermInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from short term investment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireLongtermInvestments" xlink:label="us-gaap_PaymentsToAcquireLongtermInvestments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquireLongtermInvestments" xlink:to="us-gaap_PaymentsToAcquireLongtermInvestments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsToAcquireLongtermInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to Acquire Long-Term Investments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentsToAcquireLongtermInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments on long term investment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleAndMaturityOfMarketableSecurities" xlink:label="us-gaap_ProceedsFromSaleAndMaturityOfMarketableSecurities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromSaleAndMaturityOfMarketableSecurities" xlink:to="us-gaap_ProceedsFromSaleAndMaturityOfMarketableSecurities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromSaleAndMaturityOfMarketableSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Sale and Maturity of Marketable Securities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromSaleAndMaturityOfMarketableSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Sale and Maturity of Marketable Securities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ProceedsFromSaleAndMaturityOfMarketableSecurities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redemption from marketable securities</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_AcquisitionOfNonControllingInterest" xlink:label="bgm_AcquisitionOfNonControllingInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_AcquisitionOfNonControllingInterest" xlink:to="bgm_AcquisitionOfNonControllingInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_AcquisitionOfNonControllingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to acquisition of non-controlling interest.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_AcquisitionOfNonControllingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquisition Of Non-controlling Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="bgm_AcquisitionOfNonControllingInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase of non controlling interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Cash Provided by (Used in) Investing Activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net cash used in investing activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net cash (used in) provided by investing activities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Cash Provided by (Used in) Financing Activities [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash flows from financing activities:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromRepaymentsOfLinesOfCredit" xlink:label="us-gaap_ProceedsFromRepaymentsOfLinesOfCredit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromRepaymentsOfLinesOfCredit" xlink:to="us-gaap_ProceedsFromRepaymentsOfLinesOfCredit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromRepaymentsOfLinesOfCredit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from (Repayments of) Lines of Credit</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromRepaymentsOfLinesOfCredit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from bank loans</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_ProceedsFromRepaymentsOfBankDebt" xlink:label="bgm_ProceedsFromRepaymentsOfBankDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_ProceedsFromRepaymentsOfBankDebt" xlink:to="bgm_ProceedsFromRepaymentsOfBankDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_ProceedsFromRepaymentsOfBankDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The net cash inflow or outflow for bank borrowing during the year.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_ProceedsFromRepaymentsOfBankDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from (Repayments of) bank Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_ProceedsFromRepaymentsOfBankDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayment of bank loans</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromRepaymentsOfNotesPayable" xlink:label="us-gaap_ProceedsFromRepaymentsOfNotesPayable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromRepaymentsOfNotesPayable" xlink:to="us-gaap_ProceedsFromRepaymentsOfNotesPayable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromRepaymentsOfNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from (Repayments of) Notes Payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromRepaymentsOfNotesPayable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from (Repayment of) bank notes payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromContributedCapital" xlink:label="us-gaap_ProceedsFromContributedCapital" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromContributedCapital" xlink:to="us-gaap_ProceedsFromContributedCapital_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromContributedCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Contributed Capital</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromContributedCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non controlling interest contribution</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfDividendsCommonStock" xlink:label="us-gaap_PaymentsOfDividendsCommonStock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsOfDividendsCommonStock" xlink:to="us-gaap_PaymentsOfDividendsCommonStock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsOfDividendsCommonStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments of Ordinary Dividends, Common Stock</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentsOfDividendsCommonStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dividend paid</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Cash Provided by (Used in) Financing Activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net cash provided by (used in) financing activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net cash provided by (used in) financing activities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:label="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effect of Exchange Rate on Cash, Cash Equivalents, Restricted Cash and Restricted Cash Equivalents</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effect of exchange rate change on Cash, cash equivalents and restricted cash</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effect of exchange rate on cash</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash, Cash Equivalents, Restricted Cash and Restricted Cash Equivalents, Period Increase (Decrease), Including Exchange Rate Effect</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net increase (decrease) in Cash, cash equivalents and restricted cash</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash, Cash Equivalents, Restricted Cash and Restricted Cash Equivalents</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash, cash equivalents and restricted cash at end of year</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash, cash equivalents and restricted cash at beginning of year</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SupplementalCashFlowInformationAbstract" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SupplementalCashFlowInformationAbstract" xlink:to="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Supplemental Cash Flow Information [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Supplemental cash flow information</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestPaidNet" xlink:label="us-gaap_InterestPaidNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestPaidNet" xlink:to="us-gaap_InterestPaidNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InterestPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Interest Paid, Excluding Capitalized Interest, Operating Activities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InterestPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash paid for interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxesPaidNet" xlink:label="us-gaap_IncomeTaxesPaidNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxesPaidNet" xlink:to="us-gaap_IncomeTaxesPaidNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Taxes Paid, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash paid for income taxes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:label="us-gaap_NoncashInvestingAndFinancingItemsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:to="us-gaap_NoncashInvestingAndFinancingItemsAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NoncashInvestingAndFinancingItemsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncash Investing and Financing Items [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NoncashInvestingAndFinancingItemsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Supplemental non-cash activities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueOfAssetsAcquired" xlink:label="us-gaap_FairValueOfAssetsAcquired" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueOfAssetsAcquired" xlink:to="us-gaap_FairValueOfAssetsAcquired_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueOfAssetsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value of Assets Acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueOfAssetsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unpaid RMB 15,000,000$2,107,407) of 25% euqity investment (total considerarion of RMB 25,000,000) to Caihou Capital (Shenzhen) Group</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_AdditionalPaidInCapitalDueToAdjustmentsInPreviousYears" xlink:label="bgm_AdditionalPaidInCapitalDueToAdjustmentsInPreviousYears" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_AdditionalPaidInCapitalDueToAdjustmentsInPreviousYears" xlink:to="bgm_AdditionalPaidInCapitalDueToAdjustmentsInPreviousYears_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_AdditionalPaidInCapitalDueToAdjustmentsInPreviousYears_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional paid in capital due to adjustments in previous years.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_AdditionalPaidInCapitalDueToAdjustmentsInPreviousYears_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional Paid in Capital Due to Adjustments in Previous Years</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_AdditionalPaidInCapitalDueToAdjustmentsInPreviousYears_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Additional paid-in capital due to adjustments in previous years</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_GoodwillAcquired" xlink:label="bgm_GoodwillAcquired" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_GoodwillAcquired" xlink:to="bgm_GoodwillAcquired_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_GoodwillAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of goodwill arising from the acquisition in noncash investing or financing activities.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_GoodwillAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill Acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_GoodwillAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill arising from the acquisition of the company by issuing shares 69,995,661 Class A ordinary shares per share of US$2.0</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:to="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Right-of-Use Asset Obtained in Exchange for Operating Lease Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Right of Use Assets obtained in exchange for operating lease obligations</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:to="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment, Name [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EquityMethodInvesteeNameDomain" xlink:label="srt_EquityMethodInvesteeNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_EquityMethodInvesteeNameDomain" xlink:to="srt_EquityMethodInvesteeNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_EquityMethodInvesteeNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment, Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_CaihouCapitalShenzhenGroupCo.LtdMember" xlink:label="bgm_CaihouCapitalShenzhenGroupCo.LtdMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_CaihouCapitalShenzhenGroupCo.LtdMember" xlink:to="bgm_CaihouCapitalShenzhenGroupCo.LtdMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_CaihouCapitalShenzhenGroupCo.LtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to Caihou Capital (Shenzhen) Group Co., Ltd ("Caihou").</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_CaihouCapitalShenzhenGroupCo.LtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Caihou Capital (Shenzhen) Group Co., Ltd [Member]</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAxis" xlink:label="us-gaap_BusinessAcquisitionAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionAxis" xlink:to="us-gaap_BusinessAcquisitionAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain" xlink:label="us-gaap_BusinessAcquisitionAcquireeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionAcquireeDomain" xlink:to="us-gaap_BusinessAcquisitionAcquireeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionAcquireeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition, Acquiree [Domain]</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_PatritonLimitedMember" xlink:label="bgm_PatritonLimitedMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_PatritonLimitedMember" xlink:to="bgm_PatritonLimitedMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_PatritonLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to Patriton Limited.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_PatritonLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Patriton Limited [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_PatritonLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Target Company</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_AiSolutionsAndInsuranceBusinessYxManagementCompanyLimitedAndYangLouDongMember" xlink:label="bgm_AiSolutionsAndInsuranceBusinessYxManagementCompanyLimitedAndYangLouDongMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_AiSolutionsAndInsuranceBusinessYxManagementCompanyLimitedAndYangLouDongMember" xlink:to="bgm_AiSolutionsAndInsuranceBusinessYxManagementCompanyLimitedAndYangLouDongMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_AiSolutionsAndInsuranceBusinessYxManagementCompanyLimitedAndYangLouDongMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to Company of AI Solutions and Insurance Business, YX Management Company Limited, acquisition of Yang Lou Dong.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_AiSolutionsAndInsuranceBusinessYxManagementCompanyLimitedAndYangLouDongMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">AI Solutions and Insurance Business, YX Management Company Limited and Yang Lou Dong [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_AiSolutionsAndInsuranceBusinessYxManagementCompanyLimitedAndYangLouDongMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">AI Solutions and Insurance Business, YX Management Company Limited and Yang Lou Dong</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_HmManagementCompanyLimitedMember" xlink:label="bgm_HmManagementCompanyLimitedMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_HmManagementCompanyLimitedMember" xlink:to="bgm_HmManagementCompanyLimitedMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_HmManagementCompanyLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information related to HM Management Company Limited.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_HmManagementCompanyLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">HM Management Company Limited [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_HmManagementCompanyLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">HM Management Company Limited</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_FairValueOfEquityMethodInvestmentsAcquiredAndUnpaid" xlink:label="bgm_FairValueOfEquityMethodInvestmentsAcquiredAndUnpaid" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_FairValueOfEquityMethodInvestmentsAcquiredAndUnpaid" xlink:to="bgm_FairValueOfEquityMethodInvestmentsAcquiredAndUnpaid_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_FairValueOfEquityMethodInvestmentsAcquiredAndUnpaid_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The fair value of equity method investments acquired and unpaid.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_FairValueOfEquityMethodInvestmentsAcquiredAndUnpaid_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Of Equity Method Investments Acquired And Unpaid</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_FairValueOfEquityMethodInvestmentsAcquiredAndUnpaid_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Unpaid equity investment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:label="us-gaap_EquityMethodInvestmentOwnershipPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:to="us-gaap_EquityMethodInvestmentOwnershipPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestmentOwnershipPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment, Ownership Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EquityMethodInvestmentOwnershipPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ownership interest acquired (in percent)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentAggregateCost" xlink:label="us-gaap_EquityMethodInvestmentAggregateCost" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentAggregateCost" xlink:to="us-gaap_EquityMethodInvestmentAggregateCost_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestmentAggregateCost_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment, Aggregate Cost</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EquityMethodInvestmentAggregateCost_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cost of equity method investment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_EquityMethodInvestmentAggregateCost_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total consideration</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:label="us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:to="us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition, Equity Interest Issued or Issuable, Number of Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consideration shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares issued</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionSharePrice" xlink:label="us-gaap_BusinessAcquisitionSharePrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionSharePrice" xlink:to="us-gaap_BusinessAcquisitionSharePrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionSharePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition, Share Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessAcquisitionSharePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_BusinessAcquisitionSharePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share price (in dollar per share)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:to="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ORGANIZATION AND DESCRIPTION OF BUSINESS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:to="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Organization, Consolidation and Presentation of Financial Statements Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ORGANIZATION AND DESCRIPTION OF BUSINESS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountingPoliciesAbstract" xlink:label="us-gaap_AccountingPoliciesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountingPoliciesAbstract" xlink:to="us-gaap_AccountingPoliciesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountingPoliciesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SignificantAccountingPoliciesTextBlock" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Significant Accounting Policies [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReceivablesAbstract" xlink:label="us-gaap_ReceivablesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ReceivablesAbstract" xlink:to="us-gaap_ReceivablesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ReceivablesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ACCOUNTS RECEIVABLE, NET</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:label="us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:to="us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loans, Notes, Trade and Other Receivables Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">ACCOUNTS RECEIVABLE, NET</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InventoryDisclosureAbstract" xlink:label="us-gaap_InventoryDisclosureAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommitmentsDisclosureTextBlock" xlink:label="us-gaap_CommitmentsDisclosureTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommitmentsDisclosureTextBlock" xlink:to="us-gaap_CommitmentsDisclosureTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommitmentsDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Commitments Disclosure [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommitmentsDisclosureTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">COMMITMENTS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventsAbstract" xlink:label="us-gaap_SubsequentEventsAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventsAbstract" xlink:to="us-gaap_SubsequentEventsAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventsAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SUBSEQUENT EVENTS.</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventsTextBlock" xlink:label="us-gaap_SubsequentEventsTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventsTextBlock" xlink:to="us-gaap_SubsequentEventsTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Events [Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SUBSEQUENT EVENTS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConsolidationPolicyTextBlock" xlink:label="us-gaap_ConsolidationPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConsolidationPolicyTextBlock" xlink:to="us-gaap_ConsolidationPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConsolidationPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consolidation, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConsolidationPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Basis of Presentation and Principles of Consolidation</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_RetroActivityPolicyTextBlock" xlink:label="bgm_RetroActivityPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_RetroActivityPolicyTextBlock" xlink:to="bgm_RetroActivityPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_RetroActivityPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of accounting policy for Retro activity.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_RetroActivityPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Retro Activity [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_RetroActivityPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Retroactivity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UseOfEstimates" xlink:label="us-gaap_UseOfEstimates" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_UseOfEstimates" xlink:to="us-gaap_UseOfEstimates_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_UseOfEstimates_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Use of Estimates, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_UseOfEstimates_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Use of Estimates</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_RisksAndUncertaintiesPolicyTextBlock" xlink:label="bgm_RisksAndUncertaintiesPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_RisksAndUncertaintiesPolicyTextBlock" xlink:to="bgm_RisksAndUncertaintiesPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_RisksAndUncertaintiesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of accounting policy for risks and uncertainties.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_RisksAndUncertaintiesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Risks And Uncertainties [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_RisksAndUncertaintiesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Risks and Uncertainties</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:label="us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:to="us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and Cash Equivalents, Restricted Cash and Cash Equivalents, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and Cash Equivalents</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:label="us-gaap_TradeAndOtherAccountsReceivablePolicy" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:to="us-gaap_TradeAndOtherAccountsReceivablePolicy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TradeAndOtherAccountsReceivablePolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TradeAndOtherAccountsReceivablePolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, net</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_BankAcceptanceNotesReceivablesPolicyPolicyTextBlock" xlink:label="bgm_BankAcceptanceNotesReceivablesPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_BankAcceptanceNotesReceivablesPolicyPolicyTextBlock" xlink:to="bgm_BankAcceptanceNotesReceivablesPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_BankAcceptanceNotesReceivablesPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The entire disclosure of accounting policy on bank acceptance notes receivables.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_BankAcceptanceNotesReceivablesPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bank Acceptance Notes Receivables, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_BankAcceptanceNotesReceivablesPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bank acceptance notes receivable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InventoryPolicyTextBlock" xlink:label="us-gaap_InventoryPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryPolicyTextBlock" xlink:to="us-gaap_InventoryPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InventoryPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventory, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InventoryPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventories, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:label="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:to="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_ConstructionInProgressPolicyPolicyTextBlock" xlink:label="bgm_ConstructionInProgressPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_ConstructionInProgressPolicyPolicyTextBlock" xlink:to="bgm_ConstructionInProgressPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_ConstructionInProgressPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of accounting policy Construction in progress.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_ConstructionInProgressPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Construction in Progress Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_ConstructionInProgressPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Construction in Progress</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillAndIntangibleAssetsIntangibleAssetsPolicy" xlink:label="us-gaap_GoodwillAndIntangibleAssetsIntangibleAssetsPolicy" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GoodwillAndIntangibleAssetsIntangibleAssetsPolicy" xlink:to="us-gaap_GoodwillAndIntangibleAssetsIntangibleAssetsPolicy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GoodwillAndIntangibleAssetsIntangibleAssetsPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill and Intangible Assets, Intangible Assets, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GoodwillAndIntangibleAssetsIntangibleAssetsPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible Assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeLeasesPolicyTextBlock" xlink:label="us-gaap_LesseeLeasesPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeLeasesPolicyTextBlock" xlink:to="us-gaap_LesseeLeasesPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeLeasesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Leases [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeLeasesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Leases</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesPurchasedOptionsPricePolicy" xlink:label="us-gaap_AvailableForSaleSecuritiesPurchasedOptionsPricePolicy" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AvailableForSaleSecuritiesPurchasedOptionsPricePolicy" xlink:to="us-gaap_AvailableForSaleSecuritiesPurchasedOptionsPricePolicy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AvailableForSaleSecuritiesPurchasedOptionsPricePolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Securities, Available-for-sale, Premium on Purchased Options [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AvailableForSaleSecuritiesPurchasedOptionsPricePolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment in Securities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentsPolicy" xlink:label="us-gaap_EquityMethodInvestmentsPolicy" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentsPolicy" xlink:to="us-gaap_EquityMethodInvestmentsPolicy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestmentsPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investments [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EquityMethodInvestmentsPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Term Investment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:label="us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:to="us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill and Intangible Assets, Goodwill, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Goodwill</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock" xlink:label="us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock" xlink:to="us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impairment or Disposal of Long-Lived Assets, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impairment of Long-lived Assets</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_PropertyPlantAndEquipmentPrepaymentsPolicyTextBlock" xlink:label="bgm_PropertyPlantAndEquipmentPrepaymentsPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_PropertyPlantAndEquipmentPrepaymentsPolicyTextBlock" xlink:to="bgm_PropertyPlantAndEquipmentPrepaymentsPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_PropertyPlantAndEquipmentPrepaymentsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of accounting policy for assessing and recognizing prepayments of its property, plant and equipment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_PropertyPlantAndEquipmentPrepaymentsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment, Prepayments [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_PropertyPlantAndEquipmentPrepaymentsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Prepayments for property and equipment</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_InsurancePremiumPayablesPolicyTextBlock" xlink:label="bgm_InsurancePremiumPayablesPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_InsurancePremiumPayablesPolicyTextBlock" xlink:to="bgm_InsurancePremiumPayablesPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_InsurancePremiumPayablesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of accounting policy for insurance premium payables.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_InsurancePremiumPayablesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Insurance Premium Payables [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_InsurancePremiumPayablesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Insurance premium payables</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_TransactionsWithNonControllingInterestsOfSubsidiariesPolicyTextBlock" xlink:label="bgm_TransactionsWithNonControllingInterestsOfSubsidiariesPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_TransactionsWithNonControllingInterestsOfSubsidiariesPolicyTextBlock" xlink:to="bgm_TransactionsWithNonControllingInterestsOfSubsidiariesPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_TransactionsWithNonControllingInterestsOfSubsidiariesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of accounting policy for transactions with Non-controlling interests of subsidiaries.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_TransactionsWithNonControllingInterestsOfSubsidiariesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Transactions with Non-controlling Interests of Subsidiaries [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_TransactionsWithNonControllingInterestsOfSubsidiariesPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Transactions with Non-controlling Interests of Subsidiaries</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_NonControllingInterestsPolicyTextBlock" xlink:label="bgm_NonControllingInterestsPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_NonControllingInterestsPolicyTextBlock" xlink:to="bgm_NonControllingInterestsPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_NonControllingInterestsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of accounting policy for non-controlling interests.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_NonControllingInterestsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-Controlling Interests [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_NonControllingInterestsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Non-controlling Interests</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xlink:label="us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xlink:to="us-gaap_RevenueFromContractWithCustomerPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RevenueFromContractWithCustomerPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue from Contract with Customer [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RevenueFromContractWithCustomerPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue Recognition</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_GovernmentGrantsPolicyTextBlock" xlink:label="bgm_GovernmentGrantsPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_GovernmentGrantsPolicyTextBlock" xlink:to="bgm_GovernmentGrantsPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_GovernmentGrantsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of accounting policy for government grants.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_GovernmentGrantsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Government Grants [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_GovernmentGrantsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Government Grants</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_SellingGeneralAndAdministrativeResearchAndDevelopmentExpensesPolicyPolicyTextBlock" xlink:label="bgm_SellingGeneralAndAdministrativeResearchAndDevelopmentExpensesPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_SellingGeneralAndAdministrativeResearchAndDevelopmentExpensesPolicyPolicyTextBlock" xlink:to="bgm_SellingGeneralAndAdministrativeResearchAndDevelopmentExpensesPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_SellingGeneralAndAdministrativeResearchAndDevelopmentExpensesPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Disclosure of accounting policy for Selling, General and Administrative, Research and Development Expenses.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_SellingGeneralAndAdministrativeResearchAndDevelopmentExpensesPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Selling, General and Administrative, Research and Development Expenses Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_SellingGeneralAndAdministrativeResearchAndDevelopmentExpensesPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Selling, General and Administrative, Research and Development Expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPolicyTextBlock" xlink:label="us-gaap_IncomeTaxPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxPolicyTextBlock" xlink:to="us-gaap_IncomeTaxPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeTaxPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Tax, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeTaxPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Taxes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerSharePolicyTextBlock" xlink:label="us-gaap_EarningsPerSharePolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerSharePolicyTextBlock" xlink:to="us-gaap_EarningsPerSharePolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EarningsPerSharePolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Earnings Per Share, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EarningsPerSharePolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Earnings per Share</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CompensationRelatedCostsPolicyTextBlock" xlink:label="us-gaap_CompensationRelatedCostsPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CompensationRelatedCostsPolicyTextBlock" xlink:to="us-gaap_CompensationRelatedCostsPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CompensationRelatedCostsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Compensation Related Costs, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CompensationRelatedCostsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stock Based Compensation</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:label="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:to="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Foreign Currency Transactions and Translations Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Foreign Currency Translation</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:label="us-gaap_FairValueOfFinancialInstrumentsPolicy" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:to="us-gaap_FairValueOfFinancialInstrumentsPolicy_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueOfFinancialInstrumentsPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value of Financial Instruments, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueOfFinancialInstrumentsPolicy_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value of Financial Instruments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskCreditRisk" xlink:label="us-gaap_ConcentrationRiskCreditRisk" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskCreditRisk" xlink:to="us-gaap_ConcentrationRiskCreditRisk_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskCreditRisk_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk, Credit Risk, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConcentrationRiskCreditRisk_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentrations and Credit Risk</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">New Accounting Pronouncements, Policy [Policy Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Recent Accounting Pronouncements</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetTable" xlink:label="us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetTable" xlink:to="us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consolidation, Less than Wholly Owned Subsidiary, Parent Ownership Interest, Effects of Changes, Net [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LegalEntityAxis" xlink:label="dei_LegalEntityAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_LegalEntityAxis" xlink:to="dei_LegalEntityAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_LegalEntityAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Legal Entity [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityDomain" xlink:label="dei_EntityDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityDomain" xlink:to="dei_EntityDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Entity [Domain]</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_GansuQilianshanPharmaceuticalCo.LtdMember" xlink:label="bgm_GansuQilianshanPharmaceuticalCo.LtdMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_GansuQilianshanPharmaceuticalCo.LtdMember" xlink:to="bgm_GansuQilianshanPharmaceuticalCo.LtdMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_GansuQilianshanPharmaceuticalCo.LtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Representing member information pertaining to Gansu Qilianshan Pharmaceutical Co., Ltd.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_GansuQilianshanPharmaceuticalCo.LtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gansu QLS</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_GansuQilianshanPharmaceuticalCo.LtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Gansu QLS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetLineItems" xlink:label="us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetLineItems" xlink:to="us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consolidation, Less than Wholly Owned Subsidiary, Parent Ownership Interest, Effects of Changes, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consolidation, Less than Wholly Owned Subsidiary, Parent Ownership Interest, Effects of Changes, Net</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_ScheduleOfSubsidiariesTableTextBlock" xlink:label="bgm_ScheduleOfSubsidiariesTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_ScheduleOfSubsidiariesTableTextBlock" xlink:to="bgm_ScheduleOfSubsidiariesTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_ScheduleOfSubsidiariesTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of subsidiaries.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_ScheduleOfSubsidiariesTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule Of Subsidiaries [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_ScheduleOfSubsidiariesTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of subsidiaries</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:label="us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:to="us-gaap_ScheduleOfVariableInterestEntitiesTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfVariableInterestEntitiesTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of carrying amounts of the assets, liabilities, the results of operations and cash flows of the VIE and its subsidiaries</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_ScheduleOfPropertyPlantAndEquipmentUsefulLifeTableTextBlock" xlink:label="bgm_ScheduleOfPropertyPlantAndEquipmentUsefulLifeTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_ScheduleOfPropertyPlantAndEquipmentUsefulLifeTableTextBlock" xlink:to="bgm_ScheduleOfPropertyPlantAndEquipmentUsefulLifeTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_ScheduleOfPropertyPlantAndEquipmentUsefulLifeTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Tabular disclosure of the useful life of long-lived, physical assets that are used in the normal conduct of business to produce goods and services and not intended for resale.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_ScheduleOfPropertyPlantAndEquipmentUsefulLifeTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule Of Property, Plant and Equipment, Useful Life [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_ScheduleOfPropertyPlantAndEquipmentUsefulLifeTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of estimated useful lives of the assets</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_ScheduleOfIntangibleAssetsUsefulLifeTableTextBlock" xlink:label="bgm_ScheduleOfIntangibleAssetsUsefulLifeTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_ScheduleOfIntangibleAssetsUsefulLifeTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule Of Intangible Assets, Useful Life [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_ScheduleOfIntangibleAssetsUsefulLifeTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of estimated useful lives of intangible assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RedeemableNoncontrollingInterestTableTextBlock" xlink:label="us-gaap_RedeemableNoncontrollingInterestTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RedeemableNoncontrollingInterestTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Redeemable Noncontrolling Interest [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RedeemableNoncontrollingInterestTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of shareholders' equity for the non-controlling interest from each subsidiary that is not 100% owned</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_SellingGeneralAndAdministrativeResearchAndDevelopmentExpenseTableTextBlock" xlink:label="bgm_SellingGeneralAndAdministrativeResearchAndDevelopmentExpenseTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_SellingGeneralAndAdministrativeResearchAndDevelopmentExpenseTableTextBlock" xlink:to="bgm_SellingGeneralAndAdministrativeResearchAndDevelopmentExpenseTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_SellingGeneralAndAdministrativeResearchAndDevelopmentExpenseTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Tabular disclosure of significant agreements under selling, general and administrative, research and development expense.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_SellingGeneralAndAdministrativeResearchAndDevelopmentExpenseTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Selling General And Administrative Research And Development Expense [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_SellingGeneralAndAdministrativeResearchAndDevelopmentExpenseTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of selling, general and administrative, research and development expense</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:to="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of computation of basic and diluted loss per share</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_ScheduleOfForeignCurrencyExchangeRatesTableTextBlock" xlink:label="bgm_ScheduleOfForeignCurrencyExchangeRatesTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_ScheduleOfForeignCurrencyExchangeRatesTableTextBlock" xlink:to="bgm_ScheduleOfForeignCurrencyExchangeRatesTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_ScheduleOfForeignCurrencyExchangeRatesTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Tabular disclosure of foreign exchange rates.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_ScheduleOfForeignCurrencyExchangeRatesTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule Of Foreign Currency Exchange Rates [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_ScheduleOfForeignCurrencyExchangeRatesTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of currency exchange rates</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:label="us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:to="us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of reconciliation of the beginning and ending balance of the assets and liabilities measured at fair value on recurring basis</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:label="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:to="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Accounts, Notes, Loans and Financing Receivable [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of accounts receivable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock" xlink:label="us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock" xlink:to="us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, Allowance for Credit Loss [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of change of the credit loss for doubtful accounts</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:label="us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:to="us-gaap_ScheduleOfInventoryCurrentTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfInventoryCurrentTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Inventory, Current [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfInventoryCurrentTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of inventories</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfOtherCurrentAssetsTableTextBlock" xlink:label="us-gaap_ScheduleOfOtherCurrentAssetsTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfOtherCurrentAssetsTableTextBlock" xlink:to="us-gaap_ScheduleOfOtherCurrentAssetsTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfOtherCurrentAssetsTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Other Current Assets [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfOtherCurrentAssetsTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of other current assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:label="us-gaap_PropertyPlantAndEquipmentTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:to="us-gaap_PropertyPlantAndEquipmentTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of property equipment, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:to="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Finite-Lived Intangible Assets [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of intangible assets, net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:label="us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:to="us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Finite-Lived Intangible Assets, Future Amortization Expense [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of estimated future amortization expense for intangible assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentsTextBlock" xlink:label="us-gaap_EquityMethodInvestmentsTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentsTextBlock" xlink:to="us-gaap_EquityMethodInvestmentsTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestmentsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investments [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EquityMethodInvestmentsTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of equity method investment</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_ScheduleOfShareOfResultsOfAssociatesTableTextBlock" xlink:label="bgm_ScheduleOfShareOfResultsOfAssociatesTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_ScheduleOfShareOfResultsOfAssociatesTableTextBlock" xlink:to="bgm_ScheduleOfShareOfResultsOfAssociatesTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_ScheduleOfShareOfResultsOfAssociatesTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Tabular disclosure of change of share of results of associates as part of equity method investment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_ScheduleOfShareOfResultsOfAssociatesTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Share of Results of Associates [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_ScheduleOfShareOfResultsOfAssociatesTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of change of results of associates</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock" xlink:label="us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock" xlink:to="us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of loss before income taxes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock" xlink:label="us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of significant components of the provision for income taxes</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of significant components of the income tax expense/(benefit)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:label="us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:to="us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of significant deferred tax assets and liabilities</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of significant deferred tax assets and liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:label="us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:to="us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of reconciliation of the statutory rates to the effective tax rate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of reconciliation of the statutory rates to the effective tax rate</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_ScheduleOfTaxesPayableTableTextBlock" xlink:label="bgm_ScheduleOfTaxesPayableTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_ScheduleOfTaxesPayableTableTextBlock" xlink:to="bgm_ScheduleOfTaxesPayableTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_ScheduleOfTaxesPayableTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Tabular information pertaining to taxes payable.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_ScheduleOfTaxesPayableTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of taxes payable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_ScheduleOfTaxesPayableTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of taxes payable</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_ScheduleOfWeightedAverageRemainingLeaseTermAndDiscountRateTableTextBlock" xlink:label="bgm_ScheduleOfWeightedAverageRemainingLeaseTermAndDiscountRateTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_ScheduleOfWeightedAverageRemainingLeaseTermAndDiscountRateTableTextBlock" xlink:to="bgm_ScheduleOfWeightedAverageRemainingLeaseTermAndDiscountRateTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_ScheduleOfWeightedAverageRemainingLeaseTermAndDiscountRateTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Tabular disclosure of weighted average remaining lease term and discount rate.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_ScheduleOfWeightedAverageRemainingLeaseTermAndDiscountRateTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule Of Weighted Average Remaining Lease Term And Discount Rate [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_ScheduleOfWeightedAverageRemainingLeaseTermAndDiscountRateTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of weighted average remaining lease term and discount rate</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, Maturity [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of lease liability maturities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:to="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Segment Reporting Information, by Segment [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of segment information</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ContractualObligationFiscalYearMaturityScheduleTableTextBlock" xlink:label="srt_ContractualObligationFiscalYearMaturityScheduleTableTextBlock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ContractualObligationFiscalYearMaturityScheduleTableTextBlock" xlink:to="srt_ContractualObligationFiscalYearMaturityScheduleTableTextBlock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ContractualObligationFiscalYearMaturityScheduleTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contractual Obligation, Fiscal Year Maturity [Table Text Block]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_ContractualObligationFiscalYearMaturityScheduleTableTextBlock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of contractual obligations</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_MartlineLimitedCymatrixLimitedInnovoLimitedAndTechvovoLimitedMember" xlink:label="bgm_MartlineLimitedCymatrixLimitedInnovoLimitedAndTechvovoLimitedMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_MartlineLimitedCymatrixLimitedInnovoLimitedAndTechvovoLimitedMember" xlink:to="bgm_MartlineLimitedCymatrixLimitedInnovoLimitedAndTechvovoLimitedMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_MartlineLimitedCymatrixLimitedInnovoLimitedAndTechvovoLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Martline Limited, Cymatrix Limited, Innovo Limited and Techvovo Limited.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_MartlineLimitedCymatrixLimitedInnovoLimitedAndTechvovoLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Martline Limited, Cymatrix Limited, Innovo Limited and Techvovo Limited [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_MartlineLimitedCymatrixLimitedInnovoLimitedAndTechvovoLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Martline Limited, Cymatrix Limited, Innovo Limited and Techvovo Limited</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_SuccessMythLimitedMember" xlink:label="bgm_SuccessMythLimitedMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_SuccessMythLimitedMember" xlink:to="bgm_SuccessMythLimitedMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_SuccessMythLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to Success Myth Limited.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_SuccessMythLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Success Myth Limited [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_SuccessMythLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Success Myth Limited</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipAxis" xlink:label="srt_OwnershipAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_OwnershipAxis" xlink:to="srt_OwnershipAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_OwnershipAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ownership [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipDomain" xlink:label="srt_OwnershipDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_OwnershipDomain" xlink:to="srt_OwnershipDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_OwnershipDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ownership [Domain]</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_QilianInternationalHongKongHoldingsLtdMember" xlink:label="bgm_QilianInternationalHongKongHoldingsLtdMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_QilianInternationalHongKongHoldingsLtdMember" xlink:to="bgm_QilianInternationalHongKongHoldingsLtdMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_QilianInternationalHongKongHoldingsLtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents member information pertaining to Qilian International (Hong Kong) Holdings Ltd.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_QilianInternationalHongKongHoldingsLtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Qilian HK</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_QilianInternationalHongKongHoldingsLtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Qilian HK</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_ChengduQilianTradingCo.LtdMember" xlink:label="bgm_ChengduQilianTradingCo.LtdMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_ChengduQilianTradingCo.LtdMember" xlink:to="bgm_ChengduQilianTradingCo.LtdMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_ChengduQilianTradingCo.LtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents Chengdu Qilian Trading Co., Ltd.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_ChengduQilianTradingCo.LtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Qilian Chengdu</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_ChengduQilianTradingCo.LtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Qilian Chengdu</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_ZhongqiaoYouguanECommerceServiceCo.LtdMember" xlink:label="bgm_ZhongqiaoYouguanECommerceServiceCo.LtdMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_ZhongqiaoYouguanECommerceServiceCo.LtdMember" xlink:to="bgm_ZhongqiaoYouguanECommerceServiceCo.LtdMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_ZhongqiaoYouguanECommerceServiceCo.LtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to Zhongqiao Youguan E Commerce Service Co. Ltd.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_ZhongqiaoYouguanECommerceServiceCo.LtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Zhongqiao Youguan E Commerce Service Co. Ltd [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_ZhongqiaoYouguanECommerceServiceCo.LtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Zhongqiao Youguan E Commerce Service Co. Ltd</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_JiuquanQimingBiotechnologyCo.LtdMember" xlink:label="bgm_JiuquanQimingBiotechnologyCo.LtdMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_JiuquanQimingBiotechnologyCo.LtdMember" xlink:to="bgm_JiuquanQimingBiotechnologyCo.LtdMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_JiuquanQimingBiotechnologyCo.LtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents Jiuquan Qiming Biotechnology Co., Ltd.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_JiuquanQimingBiotechnologyCo.LtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Jiuquan Qiming Biotechnology Co., Ltd</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_JiuquanQimingBiotechnologyCo.LtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Moshangfa (Gansu) Fertilizer Industry Co., Ltd (formerly Jiuquan Qiming Biotechnology Co., Ltd, "Moshangfa")</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_ChengduQilianshanBiotechnologyCo.LtdMember" xlink:label="bgm_ChengduQilianshanBiotechnologyCo.LtdMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_ChengduQilianshanBiotechnologyCo.LtdMember" xlink:to="bgm_ChengduQilianshanBiotechnologyCo.LtdMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_ChengduQilianshanBiotechnologyCo.LtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents member information pertaining to Chengdu Qilianshan Biotechnology Co., Ltd ("Chengdu QLS").</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_ChengduQilianshanBiotechnologyCo.LtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Chengdu QLS and subsidiaries</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_ChengduQilianshanBiotechnologyCo.LtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Chengdu Qilianshan Biotechnology Co., Ltd ("Chengdu QLS")</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bgm_ChengduQilianshanBiotechnologyCo.LtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Chengdu QLS and subsidiaries</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_JiuquanAhanBiotechnologyCo.Ltd.Member" xlink:label="bgm_JiuquanAhanBiotechnologyCo.Ltd.Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_JiuquanAhanBiotechnologyCo.Ltd.Member" xlink:to="bgm_JiuquanAhanBiotechnologyCo.Ltd.Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_JiuquanAhanBiotechnologyCo.Ltd.Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents member information pertaining to Jiuquan Ahan Biotechnology Co., Ltd. ("Ahan").</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_JiuquanAhanBiotechnologyCo.Ltd.Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ahan</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_JiuquanAhanBiotechnologyCo.Ltd.Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ahan</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bgm_JiuquanAhanBiotechnologyCo.Ltd.Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Jiuquan Ahan Biotechnology Co., Ltd. ("Ahan")</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_TibetCangmenTradingCo.LtdMember" xlink:label="bgm_TibetCangmenTradingCo.LtdMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_TibetCangmenTradingCo.LtdMember" xlink:to="bgm_TibetCangmenTradingCo.LtdMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_TibetCangmenTradingCo.LtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents member information pertaining to Tibet Cangmen Trading Co., Ltd ("Cangmen").</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_TibetCangmenTradingCo.LtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Tibet Cangmen Trading Co., Ltd ("Cangmen")</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_TibetCangmenTradingCo.LtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Tibet Cangmen Trading Co., Ltd ("Cangmen")</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_RugaoTianluAnimalProductsCo.LtdMember" xlink:label="bgm_RugaoTianluAnimalProductsCo.LtdMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_RugaoTianluAnimalProductsCo.LtdMember" xlink:to="bgm_RugaoTianluAnimalProductsCo.LtdMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_RugaoTianluAnimalProductsCo.LtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents member information pertaining to Rugao Tianlu Animal Products Co., Ltd ("Rugao").</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_RugaoTianluAnimalProductsCo.LtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Rugao Tianlu Animal Products Co., Ltd ("Rugao")*</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_RugaoTianluAnimalProductsCo.LtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Rugao Tianlu Animal Products Co., Ltd ("Rugao")</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_ChongqingShengfuBiologicalTechnologyCoLtdMember" xlink:label="bgm_ChongqingShengfuBiologicalTechnologyCoLtdMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_ChongqingShengfuBiologicalTechnologyCoLtdMember" xlink:to="bgm_ChongqingShengfuBiologicalTechnologyCoLtdMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_ChongqingShengfuBiologicalTechnologyCoLtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents member information pertaining to Chongqing Shengfu Biological Technology Co., Ltd ("Chongqing").</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_ChongqingShengfuBiologicalTechnologyCoLtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Chongqing Shengfu Biological Technology Co., Ltd ("Chongqing")</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_ChongqingShengfuBiologicalTechnologyCoLtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Chongqing Shengfu Biological Technology Co., Ltd ("Chongqing")</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_YxManagementCompanyLimitedMember" xlink:label="bgm_YxManagementCompanyLimitedMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_YxManagementCompanyLimitedMember" xlink:to="bgm_YxManagementCompanyLimitedMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_YxManagementCompanyLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information related to YX Management Company Limited.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_YxManagementCompanyLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">YX Management Company Limited [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_YxManagementCompanyLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">YX Management Company Limited</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_WonderDragonGlobalLimitedMember" xlink:label="bgm_WonderDragonGlobalLimitedMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_WonderDragonGlobalLimitedMember" xlink:to="bgm_WonderDragonGlobalLimitedMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_WonderDragonGlobalLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the member information pertaining to Wonder Dragon Global Limited.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_WonderDragonGlobalLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Wonder Dragon Global Limited [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_WonderDragonGlobalLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Wonder Dragon Global Limited</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_YangLouDongInternationalLimitedManagementCompanyLimitedMember" xlink:label="bgm_YangLouDongInternationalLimitedManagementCompanyLimitedMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_YangLouDongInternationalLimitedManagementCompanyLimitedMember" xlink:to="bgm_YangLouDongInternationalLimitedManagementCompanyLimitedMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_YangLouDongInternationalLimitedManagementCompanyLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to Yang Lou Dong International Limited Management Company Limited, a company duly incorporated under the laws of Hong Kong.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_YangLouDongInternationalLimitedManagementCompanyLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Yang Lou Dong International Limited Management Company Limited [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_YangLouDongInternationalLimitedManagementCompanyLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Yang Lou Dong</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:label="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:to="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition, Percentage of Voting Interests Acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Acquired equity interest, subsidiaries, percentage</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByParent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:to="us-gaap_MinorityInterestOwnershipPercentageByParent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByParent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interest, Ownership Percentage by Parent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByParent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ownership interest (in percent)</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_BusinessCombinationSharesIssuedAsConsiderationLockInPeriodForTransferOrSaleOfShares" xlink:label="bgm_BusinessCombinationSharesIssuedAsConsiderationLockInPeriodForTransferOrSaleOfShares" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_BusinessCombinationSharesIssuedAsConsiderationLockInPeriodForTransferOrSaleOfShares" xlink:to="bgm_BusinessCombinationSharesIssuedAsConsiderationLockInPeriodForTransferOrSaleOfShares_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_BusinessCombinationSharesIssuedAsConsiderationLockInPeriodForTransferOrSaleOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period of lock in time for shares issued as part of consideration after closing date for transfer or sale presented, in PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_BusinessCombinationSharesIssuedAsConsiderationLockInPeriodForTransferOrSaleOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Shares Issued As Consideration, Lock In Period For Transfer or Sale of Shares</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_BusinessCombinationSharesIssuedAsConsiderationLockInPeriodForTransferOrSaleOfShares_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period of lock in time for shares issued as part of consideration after closing date for transfer or sale</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_InitialCapital" xlink:label="bgm_InitialCapital" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_InitialCapital" xlink:to="bgm_InitialCapital_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_InitialCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of initial capital.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_InitialCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Initial Capital</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_InitialCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Initial capital</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_RegisteredCapital" xlink:label="bgm_RegisteredCapital" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_RegisteredCapital" xlink:to="bgm_RegisteredCapital_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_RegisteredCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of registered capital.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_RegisteredCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Registered Capital</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_RegisteredCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Registered capital</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_NumberOfSubsidiaries" xlink:label="bgm_NumberOfSubsidiaries" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_NumberOfSubsidiaries" xlink:to="bgm_NumberOfSubsidiaries_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_NumberOfSubsidiaries_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the number of subsidiaries.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_NumberOfSubsidiaries_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Subsidiaries</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_NumberOfSubsidiaries_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of subsidiaries</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_AmountOfPledgedEquityInterest" xlink:label="bgm_AmountOfPledgedEquityInterest" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_AmountOfPledgedEquityInterest" xlink:to="bgm_AmountOfPledgedEquityInterest_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_AmountOfPledgedEquityInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the percentage of pledged equity interest.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_AmountOfPledgedEquityInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount Of Pledged Equity Interest</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_AmountOfPledgedEquityInterest_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of pledged equity interest (in percent)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:label="us-gaap_ScheduleOfVariableInterestEntitiesTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:to="us-gaap_ScheduleOfVariableInterestEntitiesTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfVariableInterestEntitiesTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Variable Interest Entities [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidatedEntitiesAxis" xlink:label="srt_ConsolidatedEntitiesAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ConsolidatedEntitiesAxis" xlink:to="srt_ConsolidatedEntitiesAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ConsolidatedEntitiesAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consolidated Entities [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidatedEntitiesDomain" xlink:label="srt_ConsolidatedEntitiesDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ConsolidatedEntitiesDomain" xlink:to="srt_ConsolidatedEntitiesDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ConsolidatedEntitiesDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consolidated Entities [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:label="us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:to="us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">VIE and its subsidiaries</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">VIE and its subsidiaries</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableInterestEntityLineItems" xlink:label="us-gaap_VariableInterestEntityLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_VariableInterestEntityLineItems" xlink:to="us-gaap_VariableInterestEntityLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_VariableInterestEntityLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Variable Interest Entity [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_VariableInterestEntityLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Variable Interest Entity</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAbstract" xlink:label="us-gaap_LiabilitiesAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesAbstract" xlink:to="us-gaap_LiabilitiesAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Liabilities [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LiabilitiesAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">LIABILITIES</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:to="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:label="us-gaap_PropertyPlantAndEquipmentByTypeAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:to="us-gaap_PropertyPlantAndEquipmentByTypeAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentByTypeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Lived Tangible Asset [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:to="us-gaap_PropertyPlantAndEquipmentTypeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Long-Lived Tangible Asset [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LandAndBuildingMember" xlink:label="us-gaap_LandAndBuildingMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LandAndBuildingMember" xlink:to="us-gaap_LandAndBuildingMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LandAndBuildingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property and Buildings</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LandAndBuildingMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property and buildings</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MachineryAndEquipmentMember" xlink:label="us-gaap_MachineryAndEquipmentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MachineryAndEquipmentMember" xlink:to="us-gaap_MachineryAndEquipmentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MachineryAndEquipmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Machinery and equipment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MachineryAndEquipmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Machinery and equipment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AutomobilesMember" xlink:label="us-gaap_AutomobilesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AutomobilesMember" xlink:to="us-gaap_AutomobilesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AutomobilesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Automobiles</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AutomobilesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Automobiles</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_OfficeAndElectricEquipmentMember" xlink:label="bgm_OfficeAndElectricEquipmentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_OfficeAndElectricEquipmentMember" xlink:to="bgm_OfficeAndElectricEquipmentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_OfficeAndElectricEquipmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents member information pertaining to office and electric equipment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_OfficeAndElectricEquipmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Office and electric equipment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_OfficeAndElectricEquipmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Office and electric equipment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentLineItems" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentLineItems" xlink:to="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">PROPERTY AND EQUIPMENT, NET</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:label="us-gaap_PropertyPlantAndEquipmentUsefulLife" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:to="us-gaap_PropertyPlantAndEquipmentUsefulLife_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentUsefulLife_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment, Useful Life</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentUsefulLife_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Estimated useful lives (in years)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:to="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Finite-Lived Intangible Assets [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:label="us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:to="us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets by Major Class [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:label="us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:to="us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets, Major Class Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UseRightsMember" xlink:label="us-gaap_UseRightsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_UseRightsMember" xlink:to="us-gaap_UseRightsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_UseRightsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Land use rights</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_UseRightsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Land use rights</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComputerSoftwareIntangibleAssetMember" xlink:label="us-gaap_ComputerSoftwareIntangibleAssetMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ComputerSoftwareIntangibleAssetMember" xlink:to="us-gaap_ComputerSoftwareIntangibleAssetMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ComputerSoftwareIntangibleAssetMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Software</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ComputerSoftwareIntangibleAssetMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Software</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LicensingAgreementsMember" xlink:label="us-gaap_LicensingAgreementsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LicensingAgreementsMember" xlink:to="us-gaap_LicensingAgreementsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LicensingAgreementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">License for drug manufacturing</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LicensingAgreementsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">License for drug manufacturing</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:label="us-gaap_FiniteLivedIntangibleAssetsLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:to="us-gaap_FiniteLivedIntangibleAssetsLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible Assets, Net</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetUsefulLife" xlink:label="us-gaap_FiniteLivedIntangibleAssetUsefulLife" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetUsefulLife" xlink:to="us-gaap_FiniteLivedIntangibleAssetUsefulLife_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetUsefulLife_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset, Useful Life</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetUsefulLife_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Estimated useful lives (in years)</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_CashAndCashEquivalentsSubjectToExchangeRateRisks" xlink:label="bgm_CashAndCashEquivalentsSubjectToExchangeRateRisks" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_CashAndCashEquivalentsSubjectToExchangeRateRisks" xlink:to="bgm_CashAndCashEquivalentsSubjectToExchangeRateRisks_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_CashAndCashEquivalentsSubjectToExchangeRateRisks_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of cash and cash equivalents subject to exchange rate risks.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_CashAndCashEquivalentsSubjectToExchangeRateRisks_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash And Cash Equivalents Subject To Exchange Rate Risks.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_CashAndCashEquivalentsSubjectToExchangeRateRisks_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash held in PRC</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeasePracticalExpedientsPackage" xlink:label="us-gaap_LeasePracticalExpedientsPackage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LeasePracticalExpedientsPackage" xlink:to="us-gaap_LeasePracticalExpedientsPackage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LeasePracticalExpedientsPackage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lease, Practical Expedients, Package [true false]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LeasePracticalExpedientsPackage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lease, Practical expedients</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_ValueOfRemainingRedemptionAssetsInFund" xlink:label="bgm_ValueOfRemainingRedemptionAssetsInFund" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_ValueOfRemainingRedemptionAssetsInFund" xlink:to="bgm_ValueOfRemainingRedemptionAssetsInFund_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_ValueOfRemainingRedemptionAssetsInFund_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of value of remaining redemption assets in the fund.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_ValueOfRemainingRedemptionAssetsInFund_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Value of Remaining Redemption Assets in the Fund</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_ValueOfRemainingRedemptionAssetsInFund_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Value of Remaining Redemption Assets in the Fund</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_FairValueOfFund" xlink:label="bgm_FairValueOfFund" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_FairValueOfFund" xlink:to="bgm_FairValueOfFund_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_FairValueOfFund_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of fair value of the fund.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_FairValueOfFund_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value of Fund</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_FairValueOfFund_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair value of fund</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ImpairmentOfLongLivedAssetsHeldForUse" xlink:label="us-gaap_ImpairmentOfLongLivedAssetsHeldForUse" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ImpairmentOfLongLivedAssetsHeldForUse" xlink:to="us-gaap_ImpairmentOfLongLivedAssetsHeldForUse_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ImpairmentOfLongLivedAssetsHeldForUse_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impairment, Long-Lived Asset, Held-for-Use</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ImpairmentOfLongLivedAssetsHeldForUse_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Impairment loss on long-lived assets</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_ImpairmentLongLivedAssetHeldForUseStatementOfIncomeOrComprehensiveIncomeExtensibleEnumerationNotDisclosedFlag_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Boolean flag that is true when Impairment Long Lived Asset Held For Use Statement Of Income Or Comprehensive Income Extensible Enumeration Not Disclosed</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1" xlink:to="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Stockholders' Equity Note, Stock Split, Conversion Ratio</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Dilutive shares</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MinorityInterestTable" xlink:to="us-gaap_MinorityInterestTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MinorityInterestTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interest [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestLineItems" xlink:label="us-gaap_MinorityInterestLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MinorityInterestLineItems" xlink:to="us-gaap_MinorityInterestLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MinorityInterestLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interest [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MinorityInterestLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireBusinessesAndInterestInAffiliates" xlink:label="us-gaap_PaymentsToAcquireBusinessesAndInterestInAffiliates" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquireBusinessesAndInterestInAffiliates" xlink:to="us-gaap_PaymentsToAcquireBusinessesAndInterestInAffiliates_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsToAcquireBusinessesAndInterestInAffiliates_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to Acquire Businesses and Interest in Affiliates</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PaymentsToAcquireBusinessesAndInterestInAffiliates_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Payments to acquire businesses and interest in affiliates</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_PercentageOfAdditionalEquityInterestAcquired" xlink:label="bgm_PercentageOfAdditionalEquityInterestAcquired" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_PercentageOfAdditionalEquityInterestAcquired" xlink:to="bgm_PercentageOfAdditionalEquityInterestAcquired_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_PercentageOfAdditionalEquityInterestAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of additional equity interest acquired.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_PercentageOfAdditionalEquityInterestAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of Additional Equity Interest Acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_PercentageOfAdditionalEquityInterestAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of additional equity interest acquired</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:to="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Noncontrolling Interest, Ownership Percentage by Noncontrolling Owners</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ownership interest (in percent)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SellingExpense" xlink:label="us-gaap_SellingExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SellingExpense" xlink:to="us-gaap_SellingExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SellingExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Selling Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SellingExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Selling expense</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GeneralAndAdministrativeExpense" xlink:label="us-gaap_GeneralAndAdministrativeExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GeneralAndAdministrativeExpense" xlink:to="us-gaap_GeneralAndAdministrativeExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">General and Administrative Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">General and administrative expense</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_SellingGeneralAndAdministrativeResearchAndDevelopmentExpense" xlink:label="bgm_SellingGeneralAndAdministrativeResearchAndDevelopmentExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_SellingGeneralAndAdministrativeResearchAndDevelopmentExpense" xlink:to="bgm_SellingGeneralAndAdministrativeResearchAndDevelopmentExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_SellingGeneralAndAdministrativeResearchAndDevelopmentExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">It represents the value of selling, general and administrative, research and development expenses.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_SellingGeneralAndAdministrativeResearchAndDevelopmentExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Selling, General and Administrative Research and Development Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="bgm_SellingGeneralAndAdministrativeResearchAndDevelopmentExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareAbstract" xlink:label="us-gaap_EarningsPerShareAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerShareAbstract" xlink:to="us-gaap_EarningsPerShareAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EarningsPerShareAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Earnings Per Share</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEarningsPerShareDilutedByCommonClassTable" xlink:label="us-gaap_ScheduleOfEarningsPerShareDilutedByCommonClassTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfEarningsPerShareDilutedByCommonClassTable" xlink:to="us-gaap_ScheduleOfEarningsPerShareDilutedByCommonClassTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfEarningsPerShareDilutedByCommonClassTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Earnings Per Share, Diluted, by Common Class, Including Two-Class Method [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareDilutedLineItems" xlink:label="us-gaap_EarningsPerShareDilutedLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerShareDilutedLineItems" xlink:to="us-gaap_EarningsPerShareDilutedLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EarningsPerShareDilutedLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAbstract" xlink:label="us-gaap_NetIncomeLossAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLossAbstract" xlink:to="us-gaap_NetIncomeLossAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetIncomeLossAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Income (Loss) Attributable to Parent [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetIncomeLossAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Numerator:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:to="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net Income (Loss) Available to Common Stockholders, Basic</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Net loss attributable to ordinary shareholders</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xlink:to="us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted Average Number of Shares Outstanding, Diluted [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Denominator:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WeightedAverageNumberOfSharesIssuedBasic" xlink:label="us-gaap_WeightedAverageNumberOfSharesIssuedBasic" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WeightedAverageNumberOfSharesIssuedBasic" xlink:to="us-gaap_WeightedAverageNumberOfSharesIssuedBasic_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_WeightedAverageNumberOfSharesIssuedBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted Average Number of Shares Issued, Basic</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_WeightedAverageNumberOfSharesIssuedBasic_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Weighted-average number of ordinary shares outstanding - basic</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockSharesAuthorized" xlink:label="us-gaap_PreferredStockSharesAuthorized" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockSharesAuthorized" xlink:to="us-gaap_PreferredStockSharesAuthorized_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Shares Authorized</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred shares, shares authorized</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockParOrStatedValuePerShare" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockParOrStatedValuePerShare" xlink:to="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred Stock, Par or Stated Value Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferred shares, par value</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ForeignCurrencyExchangeRateTranslation1" xlink:label="us-gaap_ForeignCurrencyExchangeRateTranslation1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ForeignCurrencyExchangeRateTranslation1" xlink:to="us-gaap_ForeignCurrencyExchangeRateTranslation1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ForeignCurrencyExchangeRateTranslation1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Foreign Currency Exchange Rate, Translation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ForeignCurrencyExchangeRateTranslation1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Year-end spot rate</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_ForeignCurrencyExchangeAverageRate" xlink:label="bgm_ForeignCurrencyExchangeAverageRate" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_ForeignCurrencyExchangeAverageRate" xlink:to="bgm_ForeignCurrencyExchangeAverageRate_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_ForeignCurrencyExchangeAverageRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Foreign exchange average rate used to translate amounts denominated in functional currency to reporting currency.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_ForeignCurrencyExchangeAverageRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Foreign Currency Exchange Average Rate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_ForeignCurrencyExchangeAverageRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Average rate</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresAbstract" xlink:label="us-gaap_FairValueDisclosuresAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueDisclosuresAbstract" xlink:to="us-gaap_FairValueDisclosuresAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueDisclosuresAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value Disclosures</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisWithUnobservableInputs" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisWithUnobservableInputs" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisWithUnobservableInputs" xlink:to="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisWithUnobservableInputs_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisWithUnobservableInputs_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis with Unobservable Inputs</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisWithUnobservableInputs_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending balance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisWithUnobservableInputs_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning balance</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationPurchasesSalesIssuesSettlements" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationPurchasesSalesIssuesSettlements" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationPurchasesSalesIssuesSettlements" xlink:to="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationPurchasesSalesIssuesSettlements_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationPurchasesSalesIssuesSettlements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Inputs Reconciliation, Purchases, Sales, Issues, Settlements</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationPurchasesSalesIssuesSettlements_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase (Redemption)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationPeriodIncreaseDecrease" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationPeriodIncreaseDecrease" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationPeriodIncreaseDecrease" xlink:to="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationPeriodIncreaseDecrease_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationPeriodIncreaseDecrease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis, Unobservable Inputs Reconciliation, Period Increase (Decrease)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisUnobservableInputsReconciliationPeriodIncreaseDecrease_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Change in fair value</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_FairValueRecurringBasisAssetsAndLiabilityTransfersBetweenLevel1AndLevel2Net" xlink:label="bgm_FairValueRecurringBasisAssetsAndLiabilityTransfersBetweenLevel1AndLevel2Net" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_FairValueRecurringBasisAssetsAndLiabilityTransfersBetweenLevel1AndLevel2Net" xlink:to="bgm_FairValueRecurringBasisAssetsAndLiabilityTransfersBetweenLevel1AndLevel2Net_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_FairValueRecurringBasisAssetsAndLiabilityTransfersBetweenLevel1AndLevel2Net_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of transfers of financial instrument classified as a asset or liability transfers between level 1 and level 2 of the fair value hierarchy.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_FairValueRecurringBasisAssetsAndLiabilityTransfersBetweenLevel1AndLevel2Net_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Recurring Basis, Assets And Liability, Transfers Between Level 1 and Level 2, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_FairValueRecurringBasisAssetsAndLiabilityTransfersBetweenLevel1AndLevel2Net_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Transfer between level 1and level 2</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersNet" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersNet" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersNet" xlink:to="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersNet_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Transfers, Net</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersNet_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Asset, transfer into (out of) of level 3</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskTable" xlink:label="us-gaap_ConcentrationRiskTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskTable" xlink:to="us-gaap_ConcentrationRiskTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskByTypeAxis" xlink:label="us-gaap_ConcentrationRiskByTypeAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskByTypeAxis" xlink:to="us-gaap_ConcentrationRiskByTypeAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskByTypeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk Type [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskTypeDomain" xlink:label="us-gaap_ConcentrationRiskTypeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskTypeDomain" xlink:to="us-gaap_ConcentrationRiskTypeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskTypeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk Type [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CustomerConcentrationRiskMember" xlink:label="us-gaap_CustomerConcentrationRiskMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CustomerConcentrationRiskMember" xlink:to="us-gaap_CustomerConcentrationRiskMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CustomerConcentrationRiskMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CustomerConcentrationRiskMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SupplierConcentrationRiskMember" xlink:label="us-gaap_SupplierConcentrationRiskMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SupplierConcentrationRiskMember" xlink:to="us-gaap_SupplierConcentrationRiskMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SupplierConcentrationRiskMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Supplier</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SupplierConcentrationRiskMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Supplier</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MajorCustomersAxis" xlink:label="srt_MajorCustomersAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_MajorCustomersAxis" xlink:to="srt_MajorCustomersAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_MajorCustomersAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_NameOfMajorCustomerDomain" xlink:label="srt_NameOfMajorCustomerDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_NameOfMajorCustomerDomain" xlink:to="srt_NameOfMajorCustomerDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_NameOfMajorCustomerDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer [Domain]</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_CustomerOneMember" xlink:label="bgm_CustomerOneMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_CustomerOneMember" xlink:to="bgm_CustomerOneMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_CustomerOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents member information pertaining to customer one.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_CustomerOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer One</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_CustomerOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer One</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_CustomerTwoMember" xlink:label="bgm_CustomerTwoMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_CustomerTwoMember" xlink:to="bgm_CustomerTwoMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_CustomerTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents member information pertaining to customer two.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_CustomerTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer Two</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_CustomerTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer Two</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_CustomerThreeMember" xlink:label="bgm_CustomerThreeMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_CustomerThreeMember" xlink:to="bgm_CustomerThreeMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_CustomerThreeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents member information pertaining to customer three.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_CustomerThreeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer Three</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_CustomerThreeMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer Three</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_CustomerFourMember" xlink:label="bgm_CustomerFourMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_CustomerFourMember" xlink:to="bgm_CustomerFourMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_CustomerFourMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents member information pertaining to customer four.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_CustomerFourMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer four [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_CustomerFourMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Customer Four</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionBySupplierAxis" xlink:label="us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionBySupplierAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionBySupplierAxis" xlink:to="us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionBySupplierAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionBySupplierAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Supplier [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionSupplierDomain" xlink:label="us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionSupplierDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionSupplierDomain" xlink:to="us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionSupplierDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedGoodsAndNonemployeeServicesTransactionSupplierDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Supplier [Domain]</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_SupplierOneMember" xlink:label="bgm_SupplierOneMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_SupplierOneMember" xlink:to="bgm_SupplierOneMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_SupplierOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents member information pertaining to supplier one.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_SupplierOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Supplier One</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_SupplierOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Supplier One</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_SupplierTwoMember" xlink:label="bgm_SupplierTwoMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_SupplierTwoMember" xlink:to="bgm_SupplierTwoMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_SupplierTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents member information pertaining to supplier two.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_SupplierTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Supplier Two</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_SupplierTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Supplier Two</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:label="us-gaap_ConcentrationRiskByBenchmarkAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:to="us-gaap_ConcentrationRiskByBenchmarkAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskByBenchmarkAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk Benchmark [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskBenchmarkDomain" xlink:label="us-gaap_ConcentrationRiskBenchmarkDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskBenchmarkDomain" xlink:to="us-gaap_ConcentrationRiskBenchmarkDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskBenchmarkDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk Benchmark [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueFromContractWithCustomerMember" xlink:label="us-gaap_RevenueFromContractWithCustomerMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenueFromContractWithCustomerMember" xlink:to="us-gaap_RevenueFromContractWithCustomerMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RevenueFromContractWithCustomerMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RevenueFromContractWithCustomerMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CostOfGoodsTotalMember" xlink:label="us-gaap_CostOfGoodsTotalMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CostOfGoodsTotalMember" xlink:to="us-gaap_CostOfGoodsTotalMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CostOfGoodsTotalMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchases</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CostOfGoodsTotalMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchases</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsReceivableMember" xlink:label="us-gaap_AccountsReceivableMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableMember" xlink:to="us-gaap_AccountsReceivableMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsReceivableMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsReceivableMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsPayableMember" xlink:label="us-gaap_AccountsPayableMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsPayableMember" xlink:to="us-gaap_AccountsPayableMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsPayableMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Payable [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsPayableMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskLineItems" xlink:label="us-gaap_ConcentrationRiskLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskLineItems" xlink:to="us-gaap_ConcentrationRiskLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConcentrationRiskLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_CashAndCashEquivalentsUninsuredAmount" xlink:label="bgm_CashAndCashEquivalentsUninsuredAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_CashAndCashEquivalentsUninsuredAmount" xlink:to="bgm_CashAndCashEquivalentsUninsuredAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_CashAndCashEquivalentsUninsuredAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of cash and cash equivalents as of the balance sheet date that is not insured.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_CashAndCashEquivalentsUninsuredAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and Cash Equivalents, Uninsured Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_CashAndCashEquivalentsUninsuredAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and cash equivalents, certificates of deposit and restricted cash were on deposit at financial institutions not subject to insured</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_MaximumCashCashEquivalentsAndRestrictedCashProtectionUnderDepositProtectionScheme" xlink:label="bgm_MaximumCashCashEquivalentsAndRestrictedCashProtectionUnderDepositProtectionScheme" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_MaximumCashCashEquivalentsAndRestrictedCashProtectionUnderDepositProtectionScheme" xlink:to="bgm_MaximumCashCashEquivalentsAndRestrictedCashProtectionUnderDepositProtectionScheme_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_MaximumCashCashEquivalentsAndRestrictedCashProtectionUnderDepositProtectionScheme_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum amount of cash, cash equivalents and restricted cash deposited at financial institution in PRC that were protected under deposit protection scheme per depositor.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_MaximumCashCashEquivalentsAndRestrictedCashProtectionUnderDepositProtectionScheme_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Maximum Cash Cash Equivalents And Restricted Cash Protection Under Deposit Protection Scheme</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_MaximumCashCashEquivalentsAndRestrictedCashProtectionUnderDepositProtectionScheme_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash equivalents and restricted cash protection</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_CashAndCashEquivalentsDepositedInFinancialInstitutions" xlink:label="bgm_CashAndCashEquivalentsDepositedInFinancialInstitutions" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_CashAndCashEquivalentsDepositedInFinancialInstitutions" xlink:to="bgm_CashAndCashEquivalentsDepositedInFinancialInstitutions_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_CashAndCashEquivalentsDepositedInFinancialInstitutions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of cash and cash equivalents deposited in financial institutions.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_CashAndCashEquivalentsDepositedInFinancialInstitutions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash And Cash Equivalents, Deposited In Financial Institutions</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_CashAndCashEquivalentsDepositedInFinancialInstitutions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and cash equivalents deposited in financial institutions</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_CashAndCashEquivalentsDepositedInFinancialInstitutionsAnnualLimit" xlink:label="bgm_CashAndCashEquivalentsDepositedInFinancialInstitutionsAnnualLimit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_CashAndCashEquivalentsDepositedInFinancialInstitutionsAnnualLimit" xlink:to="bgm_CashAndCashEquivalentsDepositedInFinancialInstitutionsAnnualLimit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_CashAndCashEquivalentsDepositedInFinancialInstitutionsAnnualLimit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of cash and cash equivalents deposited in financial institution subject to annual limit.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_CashAndCashEquivalentsDepositedInFinancialInstitutionsAnnualLimit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash And Cash Equivalents, Deposited In Financial Institutions, Annual Limit</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_CashAndCashEquivalentsDepositedInFinancialInstitutionsAnnualLimit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash and cash equivalents deposited in financial institutions annual limit</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashFDICInsuredAmount" xlink:label="us-gaap_CashFDICInsuredAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashFDICInsuredAmount" xlink:to="us-gaap_CashFDICInsuredAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashFDICInsuredAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash, FDIC Insured Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashFDICInsuredAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cash deposited in FI insured by FDIC</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_NumberOfCustomers" xlink:label="bgm_NumberOfCustomers" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_NumberOfCustomers" xlink:to="bgm_NumberOfCustomers_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_NumberOfCustomers_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the number of customer.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_NumberOfCustomers_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Customers</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_NumberOfCustomers_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of customers</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskPercentage1" xlink:label="us-gaap_ConcentrationRiskPercentage1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskPercentage1" xlink:to="us-gaap_ConcentrationRiskPercentage1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskPercentage1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration Risk, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ConcentrationRiskPercentage1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Concentration risk (in percent)</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_NumberOfVendors" xlink:label="bgm_NumberOfVendors" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_NumberOfVendors" xlink:to="bgm_NumberOfVendors_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_NumberOfVendors_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the number of vendor.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_NumberOfVendors_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number Of Vendors</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bgm_NumberOfVendors_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of vendors</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_PercentageOfAccountsPayableOutstandingFromTransactionWithSupplier" xlink:label="bgm_PercentageOfAccountsPayableOutstandingFromTransactionWithSupplier" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_PercentageOfAccountsPayableOutstandingFromTransactionWithSupplier" xlink:to="bgm_PercentageOfAccountsPayableOutstandingFromTransactionWithSupplier_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_PercentageOfAccountsPayableOutstandingFromTransactionWithSupplier_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of percentage of accounts payable outstanding from transaction with supplier.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_PercentageOfAccountsPayableOutstandingFromTransactionWithSupplier_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of Accounts Payable Outstanding From Transaction with Supplier</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_PercentageOfAccountsPayableOutstandingFromTransactionWithSupplier_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of accounts payable outstanding from transaction with supplier</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsReceivableGrossCurrent" xlink:label="us-gaap_AccountsReceivableGrossCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableGrossCurrent" xlink:to="us-gaap_AccountsReceivableGrossCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsReceivableGrossCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, before Allowance for Credit Loss, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsReceivableGrossCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Trade accounts receivable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:to="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, Allowance for Credit Loss, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less: allowances for credit loss</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:to="us-gaap_AllowanceForDoubtfulAccountsReceivable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Accounts Receivable, Allowance for Credit Loss</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending balance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning balance</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_IncreaseDecreaseInAllowanceForDoubtfulAccountsReceivable" xlink:label="bgm_IncreaseDecreaseInAllowanceForDoubtfulAccountsReceivable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_IncreaseDecreaseInAllowanceForDoubtfulAccountsReceivable" xlink:to="bgm_IncreaseDecreaseInAllowanceForDoubtfulAccountsReceivable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_IncreaseDecreaseInAllowanceForDoubtfulAccountsReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The increase (decrease) during the reporting period in allowance for doubtful accounts receivables.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_IncreaseDecreaseInAllowanceForDoubtfulAccountsReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Increase Decrease In Allowance For Doubtful Accounts Receivable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bgm_IncreaseDecreaseInAllowanceForDoubtfulAccountsReceivable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Addition</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_AllowancesForDoubtfulAccountsExchangeRateDifferences" xlink:label="bgm_AllowancesForDoubtfulAccountsExchangeRateDifferences" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_AllowancesForDoubtfulAccountsExchangeRateDifferences" xlink:to="bgm_AllowancesForDoubtfulAccountsExchangeRateDifferences_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_AllowancesForDoubtfulAccountsExchangeRateDifferences_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of exchange rate effect changes on allowances for doubtful accounts receivables.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_AllowancesForDoubtfulAccountsExchangeRateDifferences_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Allowances For Doubtful Accounts, Exchange Rate Differences</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_AllowancesForDoubtfulAccountsExchangeRateDifferences_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Exchange rate difference</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InventoryRawMaterialsAndSupplies" xlink:label="us-gaap_InventoryRawMaterialsAndSupplies" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryRawMaterialsAndSupplies" xlink:to="us-gaap_InventoryRawMaterialsAndSupplies_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InventoryRawMaterialsAndSupplies_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventory, Raw Materials and Supplies, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InventoryRawMaterialsAndSupplies_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Raw materials</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InventoryWorkInProcess" xlink:label="us-gaap_InventoryWorkInProcess" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryWorkInProcess" xlink:to="us-gaap_InventoryWorkInProcess_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InventoryWorkInProcess_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventory, Work in Process, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InventoryWorkInProcess_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Work-in-progress</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InventoryFinishedGoods" xlink:label="us-gaap_InventoryFinishedGoods" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryFinishedGoods" xlink:to="us-gaap_InventoryFinishedGoods_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InventoryFinishedGoods_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Inventory, Finished Goods, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InventoryFinishedGoods_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finished goods</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherReceivablesNetCurrent" xlink:label="us-gaap_OtherReceivablesNetCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherReceivablesNetCurrent" xlink:to="us-gaap_OtherReceivablesNetCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherReceivablesNetCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Receivables, Net, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherReceivablesNetCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other receivables</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ValueAddedTaxReceivableCurrent" xlink:label="us-gaap_ValueAddedTaxReceivableCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ValueAddedTaxReceivableCurrent" xlink:to="us-gaap_ValueAddedTaxReceivableCurrent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ValueAddedTaxReceivableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Value Added Tax Receivable, Current</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ValueAddedTaxReceivableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Input VAT</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCapitalizedPropertyPlantAndEquipmentMember" xlink:label="us-gaap_OtherCapitalizedPropertyPlantAndEquipmentMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherCapitalizedPropertyPlantAndEquipmentMember" xlink:to="us-gaap_OtherCapitalizedPropertyPlantAndEquipmentMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherCapitalizedPropertyPlantAndEquipmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Capitalized Property Plant and Equipment [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherCapitalizedPropertyPlantAndEquipmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Others</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_QilianChengduMember" xlink:label="bgm_QilianChengduMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_QilianChengduMember" xlink:to="bgm_QilianChengduMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_QilianChengduMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to Qilian Chengdu.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_QilianChengduMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Qilian Chengdu [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_QilianChengduMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Qilian Chengdu</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_PropertyPlantAndEquipmentExcludingConstructionInProgressGross" xlink:label="bgm_PropertyPlantAndEquipmentExcludingConstructionInProgressGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_PropertyPlantAndEquipmentExcludingConstructionInProgressGross" xlink:to="bgm_PropertyPlantAndEquipmentExcludingConstructionInProgressGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_PropertyPlantAndEquipmentExcludingConstructionInProgressGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount excluding construction in progress before accumulated depreciation, depletion and amortization of physical assets used in the normal conduct of business and not intended for resale. Examples include, but are not limited to, land, buildings, machinery and equipment, office equipment, and furniture and fixtures.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_PropertyPlantAndEquipmentExcludingConstructionInProgressGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property, Plant and Equipment Excluding Construction In Progress, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_PropertyPlantAndEquipmentExcludingConstructionInProgressGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subtotal</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_PropertyPlantAndEquipmentExcludingConstructionInProgressAccumulatedDepreciation" xlink:label="bgm_PropertyPlantAndEquipmentExcludingConstructionInProgressAccumulatedDepreciation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_PropertyPlantAndEquipmentExcludingConstructionInProgressAccumulatedDepreciation" xlink:to="bgm_PropertyPlantAndEquipmentExcludingConstructionInProgressAccumulatedDepreciation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_PropertyPlantAndEquipmentExcludingConstructionInProgressAccumulatedDepreciation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of property plant and equipment, excluding construction in progress, accumulated depreciation.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_PropertyPlantAndEquipmentExcludingConstructionInProgressAccumulatedDepreciation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property Plant and Equipment, Excluding Construction in Progress, Accumulated Depreciation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="bgm_PropertyPlantAndEquipmentExcludingConstructionInProgressAccumulatedDepreciation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less: accumulated depreciation</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_PropertyPlantAndEquipmentExcludingConstructionInProgressAccumulatedImpairment" xlink:label="bgm_PropertyPlantAndEquipmentExcludingConstructionInProgressAccumulatedImpairment" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_PropertyPlantAndEquipmentExcludingConstructionInProgressAccumulatedImpairment" xlink:to="bgm_PropertyPlantAndEquipmentExcludingConstructionInProgressAccumulatedImpairment_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_PropertyPlantAndEquipmentExcludingConstructionInProgressAccumulatedImpairment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of property plant and equipment, excluding construction in progress, accumulated impairment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_PropertyPlantAndEquipmentExcludingConstructionInProgressAccumulatedImpairment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property Plant and Equipment, Excluding Construction in Progress, Accumulated Impairment</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="bgm_PropertyPlantAndEquipmentExcludingConstructionInProgressAccumulatedImpairment_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less: accumulated impairment</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Depreciation" xlink:label="us-gaap_Depreciation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Depreciation" xlink:to="us-gaap_Depreciation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Depreciation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Depreciation</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_Depreciation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Depreciation expense</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_PropertyAndEquipmentReceivedAgainstPrepayments" xlink:label="bgm_PropertyAndEquipmentReceivedAgainstPrepayments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_PropertyAndEquipmentReceivedAgainstPrepayments" xlink:to="bgm_PropertyAndEquipmentReceivedAgainstPrepayments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_PropertyAndEquipmentReceivedAgainstPrepayments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of property and equipment received and accepted against prepayments.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_PropertyAndEquipmentReceivedAgainstPrepayments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property and Equipment Received Against Prepayments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_PropertyAndEquipmentReceivedAgainstPrepayments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Property received and accepted out of Prepayments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsGross" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsGross" xlink:to="us-gaap_FiniteLivedIntangibleAssetsGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Assets, Accumulated Amortization</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AmortizationOfIntangibleAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amortization expense</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseAbstract" xlink:label="us-gaap_FiniteLivedIntangibleAssetsFutureAmortizationExpenseAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset, Expected Amortization, Year One</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset, Expected Amortization, Year Two</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset, Expected Amortization, Year Three</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2028</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Finite-Lived Intangible Asset, Expected Amortization, Year Four</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2029</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_IntangibleAssetFiniteLivedEstimatedAmortizationExpenseAfterYearFour" xlink:label="bgm_IntangibleAssetFiniteLivedEstimatedAmortizationExpenseAfterYearFour" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_IntangibleAssetFiniteLivedEstimatedAmortizationExpenseAfterYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of amortization expense for finite-lived intangible asset expected to be recognized after fourth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach). Excludes goodwill and capitalized cost for software to be sold, leased, or marketed.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_IntangibleAssetFiniteLivedEstimatedAmortizationExpenseAfterYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Intangible Asset, Finite-Lived, Estimated Amortization Expense, after Year Four</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_IntangibleAssetFiniteLivedEstimatedAmortizationExpenseAfterYearFour_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Thereafter</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Equity Method Investments [Table]</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_FanhuaInsuranceSurveyorsLossAdjustersCo.LtdMember" xlink:label="bgm_FanhuaInsuranceSurveyorsLossAdjustersCo.LtdMember" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity method investment</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_EquityMethodInvestmentOwnershipPercentageSold" xlink:label="bgm_EquityMethodInvestmentOwnershipPercentageSold" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investments</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentSoldCarryingAmount" xlink:label="us-gaap_EquityMethodInvestmentSoldCarryingAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentSoldCarryingAmount" xlink:to="us-gaap_EquityMethodInvestmentSoldCarryingAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestmentSoldCarryingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment, Amount Sold</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_EquityMethodInvestmentSoldCarryingAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Investment disposed</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_EquityMethodInvestmentGainLossDueToForeignExchangeRateDifference" xlink:label="bgm_EquityMethodInvestmentGainLossDueToForeignExchangeRateDifference" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_EquityMethodInvestmentGainLossDueToForeignExchangeRateDifference" xlink:to="bgm_EquityMethodInvestmentGainLossDueToForeignExchangeRateDifference_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_EquityMethodInvestmentGainLossDueToForeignExchangeRateDifference_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">This element represents disclosure of the amount of gain (loss) due to foreign exchange rate difference.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_EquityMethodInvestmentGainLossDueToForeignExchangeRateDifference_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment, Gain (Loss) Due to Foreign Exchange Rate Difference</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_EquityMethodInvestmentGainLossDueToForeignExchangeRateDifference_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Exchange rate difference</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_EquityMethodInvestmentShareOfResultsOfAssociates" xlink:label="bgm_EquityMethodInvestmentShareOfResultsOfAssociates" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_EquityMethodInvestmentShareOfResultsOfAssociates" xlink:to="bgm_EquityMethodInvestmentShareOfResultsOfAssociates_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_EquityMethodInvestmentShareOfResultsOfAssociates_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of share of results of associates as part of equity method investment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_EquityMethodInvestmentShareOfResultsOfAssociates_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment, Share Of Results Of Associates</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="bgm_EquityMethodInvestmentShareOfResultsOfAssociates_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ending balance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="bgm_EquityMethodInvestmentShareOfResultsOfAssociates_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Beginning balance</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_EquityMethodInvestmentShareOfResultsOfAssociatesAddition" xlink:label="bgm_EquityMethodInvestmentShareOfResultsOfAssociatesAddition" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_EquityMethodInvestmentShareOfResultsOfAssociatesAddition" xlink:to="bgm_EquityMethodInvestmentShareOfResultsOfAssociatesAddition_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_EquityMethodInvestmentShareOfResultsOfAssociatesAddition_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of recognized share of results of associates.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_EquityMethodInvestmentShareOfResultsOfAssociatesAddition_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Method Investment, Share of Results of Associates, Addition</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_EquityMethodInvestmentShareOfResultsOfAssociatesAddition_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Addition</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfShortTermDebtTable" xlink:label="us-gaap_ScheduleOfShortTermDebtTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfShortTermDebtTable" xlink:to="us-gaap_ScheduleOfShortTermDebtTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfShortTermDebtTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Short-term Debt [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortTermDebtTypeAxis" xlink:label="us-gaap_ShortTermDebtTypeAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShortTermDebtTypeAxis" xlink:to="us-gaap_ShortTermDebtTypeAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShortTermDebtTypeAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Short-term Debt, Type [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortTermDebtTypeDomain" xlink:label="us-gaap_ShortTermDebtTypeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShortTermDebtTypeDomain" xlink:to="us-gaap_ShortTermDebtTypeDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShortTermDebtTypeDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Short-term Debt, Type [Domain]</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_LoanAgreementWithPostalSavingsBankOfChinaMember" xlink:label="bgm_LoanAgreementWithPostalSavingsBankOfChinaMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_LoanAgreementWithPostalSavingsBankOfChinaMember" xlink:to="bgm_LoanAgreementWithPostalSavingsBankOfChinaMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_LoanAgreementWithPostalSavingsBankOfChinaMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to loan agreement with Postal Savings Bank of China.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_LoanAgreementWithPostalSavingsBankOfChinaMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loan Agreement With Postal Savings Bank of China [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_LoanAgreementWithPostalSavingsBankOfChinaMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loan agreement with Postal Savings Bank of China</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_LoanAgreementWithAgriculturalBankOfChinaMember" xlink:label="bgm_LoanAgreementWithAgriculturalBankOfChinaMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_LoanAgreementWithAgriculturalBankOfChinaMember" xlink:to="bgm_LoanAgreementWithAgriculturalBankOfChinaMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_LoanAgreementWithAgriculturalBankOfChinaMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to loan agreement with Agricultural Bank of China.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_LoanAgreementWithAgriculturalBankOfChinaMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loan Agreement With Agricultural Bank of China [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_LoanAgreementWithAgriculturalBankOfChinaMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loan agreement with Agricultural Bank of China</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_LoanAgreementWithChongqingRuralCommercialBankMember" xlink:label="bgm_LoanAgreementWithChongqingRuralCommercialBankMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_LoanAgreementWithChongqingRuralCommercialBankMember" xlink:to="bgm_LoanAgreementWithChongqingRuralCommercialBankMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_LoanAgreementWithChongqingRuralCommercialBankMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to loan agreement with Chongqing Rural Commercial Bank.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_LoanAgreementWithChongqingRuralCommercialBankMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loan Agreement With Chongqing Rural Commercial Bank[Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_LoanAgreementWithChongqingRuralCommercialBankMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loan agreement with Chongqing Rural Commercial Bank</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortTermDebtLineItems" xlink:label="us-gaap_ShortTermDebtLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShortTermDebtLineItems" xlink:to="us-gaap_ShortTermDebtLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShortTermDebtLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Short-term Debt [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShortTermDebtLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Bank Loans</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentFaceAmount" xlink:label="us-gaap_DebtInstrumentFaceAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentFaceAmount" xlink:to="us-gaap_DebtInstrumentFaceAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Face Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Loan agreement amount</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:to="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Interest Rate, Stated Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Fixed interest rate (in percent)</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentTerm" xlink:label="us-gaap_DebtInstrumentTerm" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentTerm" xlink:to="us-gaap_DebtInstrumentTerm_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Debt Instrument, Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Term of loan agreement</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RepaymentsOfDebt" xlink:label="us-gaap_RepaymentsOfDebt" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RepaymentsOfDebt" xlink:to="us-gaap_RepaymentsOfDebt_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RepaymentsOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayments of Debt</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RepaymentsOfDebt_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Repayment of loan</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationTable" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EffectiveIncomeTaxRateReconciliationTable" xlink:to="us-gaap_EffectiveIncomeTaxRateReconciliationTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective Income Tax Rate Reconciliation [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StatementGeographicalAxis" xlink:label="srt_StatementGeographicalAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_StatementGeographicalAxis" xlink:to="srt_StatementGeographicalAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_StatementGeographicalAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Geographical [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_SegmentGeographicalDomain" xlink:label="srt_SegmentGeographicalDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_SegmentGeographicalDomain" xlink:to="srt_SegmentGeographicalDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_SegmentGeographicalDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Geographical [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/country/2025/country-2025.xsd#country_HK" xlink:label="country_HK" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="country_HK" xlink:to="country_HK_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="country_HK_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Hong Kong</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="country_HK_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Hong Kong</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/country/2025/country-2025.xsd#country_CN" xlink:label="country_CN" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="country_CN" xlink:to="country_CN_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="country_CN_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">China</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="country_CN_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">China</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_WesternRegionMember" xlink:label="bgm_WesternRegionMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_WesternRegionMember" xlink:to="bgm_WesternRegionMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_WesternRegionMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to Western Region.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_WesternRegionMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Western Region</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_WesternRegionMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Western Region</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StatementScenarioAxis" xlink:label="srt_StatementScenarioAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_StatementScenarioAxis" xlink:to="srt_StatementScenarioAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_StatementScenarioAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Scenario [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScenarioUnspecifiedDomain" xlink:label="srt_ScenarioUnspecifiedDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ScenarioUnspecifiedDomain" xlink:to="srt_ScenarioUnspecifiedDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ScenarioUnspecifiedDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Scenario [Domain]</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_ScenarioOneMember" xlink:label="bgm_ScenarioOneMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_ScenarioOneMember" xlink:to="bgm_ScenarioOneMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_ScenarioOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to scenario one.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_ScenarioOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Scenario One</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_ScenarioOneMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Scenario One</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_ScenarioTwoMember" xlink:label="bgm_ScenarioTwoMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_ScenarioTwoMember" xlink:to="bgm_ScenarioTwoMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_ScenarioTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to scenario two.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_ScenarioTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Scenario Two</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_ScenarioTwoMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Scenario Two</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_TaxRateForMicroAndSmallEnterprisesMember" xlink:label="bgm_TaxRateForMicroAndSmallEnterprisesMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_TaxRateForMicroAndSmallEnterprisesMember" xlink:to="bgm_TaxRateForMicroAndSmallEnterprisesMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_TaxRateForMicroAndSmallEnterprisesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to a scenario specifying tax rate applicable to Micro and Small Enterprise.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_TaxRateForMicroAndSmallEnterprisesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Tax Rate For Micro And Small Enterprises [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_TaxRateForMicroAndSmallEnterprisesMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Tax rate for Micro and Small Enterprise</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_WhenTaxableIncomeDoesNotExceed3000000Member" xlink:label="bgm_WhenTaxableIncomeDoesNotExceed3000000Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_WhenTaxableIncomeDoesNotExceed3000000Member" xlink:to="bgm_WhenTaxableIncomeDoesNotExceed3000000Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_WhenTaxableIncomeDoesNotExceed3000000Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information Represents information pertaining to a scenario specifying when taxable income is within 3,000,000 for a small low-profit enterprise. pertaining to a scenario specifying tax rate applicable to Micro and Small Enterprise.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_WhenTaxableIncomeDoesNotExceed3000000Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">When Taxable Income Does Not Exceed 3,000,000 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_WhenTaxableIncomeDoesNotExceed3000000Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Taxable income does not exceed 3,000,000</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_WhenTaxableIncomeExceeds3000000Member" xlink:label="bgm_WhenTaxableIncomeExceeds3000000Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_WhenTaxableIncomeExceeds3000000Member" xlink:to="bgm_WhenTaxableIncomeExceeds3000000Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_WhenTaxableIncomeExceeds3000000Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to a scenario specifying when taxable income exceeds 3,000,000 for a small low-profit enterprise.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_WhenTaxableIncomeExceeds3000000Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">When Taxable Income Exceeds 3,000,000 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_WhenTaxableIncomeExceeds3000000Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Taxable income exceed 3,000,000</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationLineItems" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EffectiveIncomeTaxRateReconciliationLineItems" xlink:to="us-gaap_EffectiveIncomeTaxRateReconciliationLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective Income Tax Rate Reconciliation [Line Items]</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_IncomeTaxPreferentialTaxRate" xlink:label="bgm_IncomeTaxPreferentialTaxRate" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_IncomeTaxPreferentialTaxRate" xlink:to="bgm_IncomeTaxPreferentialTaxRate_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_IncomeTaxPreferentialTaxRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of the preferential tax rate applicable to the entity under the preferential tax treatment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_IncomeTaxPreferentialTaxRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Tax, Preferential Tax Rate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_IncomeTaxPreferentialTaxRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Favorable tax rate (as a percent)</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_BaseProfitForCalculatingTaxRate" xlink:label="bgm_BaseProfitForCalculatingTaxRate" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_BaseProfitForCalculatingTaxRate" xlink:to="bgm_BaseProfitForCalculatingTaxRate_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_BaseProfitForCalculatingTaxRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of profit for calculating tax rate.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_BaseProfitForCalculatingTaxRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Base Profit For Calculating Tax Rate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_BaseProfitForCalculatingTaxRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Base profit for calculating tax rate</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_ThresholdAnnualTaxableIncome" xlink:label="bgm_ThresholdAnnualTaxableIncome" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_ThresholdAnnualTaxableIncome" xlink:to="bgm_ThresholdAnnualTaxableIncome_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_ThresholdAnnualTaxableIncome_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold annual taxable income considered as basis for tax rate.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_ThresholdAnnualTaxableIncome_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Threshold Annual Taxable Income</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_ThresholdAnnualTaxableIncome_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Annual taxable income</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:to="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective Income Tax Rate Reconciliation, at Federal Statutory Income Tax Rate, Percent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">China Statutory income tax rate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Statutory income tax rate (in percent)</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_IncomeTaxFavorableTaxRate" xlink:label="bgm_IncomeTaxFavorableTaxRate" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_IncomeTaxFavorableTaxRate" xlink:to="bgm_IncomeTaxFavorableTaxRate_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_IncomeTaxFavorableTaxRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of favorable income tax rate.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_IncomeTaxFavorableTaxRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income Tax Favorable Tax Rate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_IncomeTaxFavorableTaxRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Favorable tax rate (in percent)</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_PreferentialIncomeTaxRate" xlink:label="bgm_PreferentialIncomeTaxRate" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_PreferentialIncomeTaxRate" xlink:to="bgm_PreferentialIncomeTaxRate_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_PreferentialIncomeTaxRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of preferential income tax rate.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_PreferentialIncomeTaxRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferential Income Tax Rate</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_PreferentialIncomeTaxRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Preferential tax rate (in percent)</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_EnterpriseIncomeTaxRatePercentage" xlink:label="bgm_EnterpriseIncomeTaxRatePercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_EnterpriseIncomeTaxRatePercentage" xlink:to="bgm_EnterpriseIncomeTaxRatePercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_EnterpriseIncomeTaxRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of applicable enterprise income tax rate.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_EnterpriseIncomeTaxRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Enterprise Income Tax Rate, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_EnterpriseIncomeTaxRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Enterprise taxable income (in percent)</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_FavorableIncomeTaxRatePercentage" xlink:label="bgm_FavorableIncomeTaxRatePercentage" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_FavorableIncomeTaxRatePercentage" xlink:to="bgm_FavorableIncomeTaxRatePercentage_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_FavorableIncomeTaxRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The percentage of favorable income tax rate applicable to the company.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_FavorableIncomeTaxRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Favorable Income Tax Rate, Percentage</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_FavorableIncomeTaxRatePercentage_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Favorable income tax (in percent)</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_WithholdingTaxRateOnDividendDistributions" xlink:label="bgm_WithholdingTaxRateOnDividendDistributions" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_WithholdingTaxRateOnDividendDistributions" xlink:to="bgm_WithholdingTaxRateOnDividendDistributions_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_WithholdingTaxRateOnDividendDistributions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of withholding tax rate on dividend distributions.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_WithholdingTaxRateOnDividendDistributions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Withholding Tax Rate On Dividend Distributions</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_WithholdingTaxRateOnDividendDistributions_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Withholding tax rate</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/country/2025/country-2025.xsd#country_KY" xlink:label="country_KY" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="country_KY" xlink:to="country_KY_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="country_KY_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cayman Islands</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="country_KY_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Cayman Islands</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossAttributableToParent" xlink:label="us-gaap_IncomeLossAttributableToParent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeLossAttributableToParent" xlink:to="us-gaap_IncomeLossAttributableToParent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeLossAttributableToParent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income (Loss) Attributable to Parent, before Tax</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeLossAttributableToParent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Income (loss) before income taxes</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:label="us-gaap_CurrentIncomeTaxExpenseBenefit" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:to="us-gaap_CurrentIncomeTaxExpenseBenefit_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CurrentIncomeTaxExpenseBenefit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Current Income Tax Expense (Benefit)</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CurrentIncomeTaxExpenseBenefit_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Current income taxes</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_DeferredIncomeTaxBenefitExpense" xlink:label="bgm_DeferredIncomeTaxBenefitExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_DeferredIncomeTaxBenefitExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of deferred income tax expense (benefit) pertaining to income (loss) from continuing operations.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_DeferredIncomeTaxBenefitExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Income Tax Benefit Expense</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsNetAbstract" xlink:label="us-gaap_DeferredTaxAssetsNetAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredTaxAssetsNetAbstract" xlink:to="us-gaap_DeferredTaxAssetsNetAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredTaxAssetsNetAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred tax assets:</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsAllowanceForDoubtfulAccountsAndInventoryProvision" xlink:label="bgm_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsAllowanceForDoubtfulAccountsAndInventoryProvision" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsAllowanceForDoubtfulAccountsAndInventoryProvision_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount before allocation of valuation allowances of deferred tax asset attributable to deductible temporary differences from the allowance for doubtful accounts and inventory provision.</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:label="us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Tax Assets, Operating Loss Carryforwards</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">NOL Carryforwards</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsDeferredIncome" xlink:label="us-gaap_DeferredTaxAssetsDeferredIncome" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredTaxAssetsDeferredIncome" xlink:to="us-gaap_DeferredTaxAssetsDeferredIncome_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredTaxAssetsDeferredIncome_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Tax Assets, Deferred Income</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_DeferredTaxAssetsDeferredIncome_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred government grants</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsGross" xlink:label="us-gaap_DeferredTaxAssetsGross" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredTaxAssetsGross" xlink:to="us-gaap_DeferredTaxAssetsGross_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredTaxAssetsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred Tax Assets, Gross</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_DeferredTaxAssetsGross_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total deferred tax assets</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract" xlink:to="us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective Income Tax Rate Reconciliation, Percent [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Reconciles the statutory rates, Percent</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationChangeInEnactedTaxRate" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationChangeInEnactedTaxRate" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EffectiveIncomeTaxRateReconciliationChangeInEnactedTaxRate" xlink:to="us-gaap_EffectiveIncomeTaxRateReconciliationChangeInEnactedTaxRate_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationChangeInEnactedTaxRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective Income Tax Rate Reconciliation, Change in Enacted Tax Rate, Percent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationChangeInEnactedTaxRate_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effect of favorable income tax rate in the PRC</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential" xlink:to="us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective Income Tax Rate Reconciliation, Foreign Income Tax Rate Differential, Percent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Tax rate difference in jurisdictions other than PRC</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsResearch" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsResearch" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsResearch" xlink:to="us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsResearch_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsResearch_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective Income Tax Rate Reconciliation, Tax Credit, Research, Percent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsResearch_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">R&amp;D credit</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_EffectiveIncomeTaxRateReconciliationNetOperatingLossCarryforwardPercent" xlink:label="bgm_EffectiveIncomeTaxRateReconciliationNetOperatingLossCarryforwardPercent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_EffectiveIncomeTaxRateReconciliationNetOperatingLossCarryforwardPercent" xlink:to="bgm_EffectiveIncomeTaxRateReconciliationNetOperatingLossCarryforwardPercent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_EffectiveIncomeTaxRateReconciliationNetOperatingLossCarryforwardPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to effect of net operating loss carryforwards.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_EffectiveIncomeTaxRateReconciliationNetOperatingLossCarryforwardPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective Income Tax Rate Reconciliation, Net Operating Loss Carryforward, Percent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_EffectiveIncomeTaxRateReconciliationNetOperatingLossCarryforwardPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effect of NOL carryforward</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_EffectiveIncomeTaxRateReconciliationDeferredTaxProvisionPercent" xlink:label="bgm_EffectiveIncomeTaxRateReconciliationDeferredTaxProvisionPercent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_EffectiveIncomeTaxRateReconciliationDeferredTaxProvisionPercent" xlink:to="bgm_EffectiveIncomeTaxRateReconciliationDeferredTaxProvisionPercent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_EffectiveIncomeTaxRateReconciliationDeferredTaxProvisionPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to deferred tax provision.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_EffectiveIncomeTaxRateReconciliationDeferredTaxProvisionPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective Income Tax Rate Reconciliation, Deferred Tax Provision, Percent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_EffectiveIncomeTaxRateReconciliationDeferredTaxProvisionPercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred tax provision</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective Income Tax Rate Reconciliation, Change in Deferred Tax Assets Valuation Allowance, Percent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Deferred tax allowance</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_EffectiveIncomeTaxRateReconciliationNonDeductiblePermanentDifferences" xlink:label="bgm_EffectiveIncomeTaxRateReconciliationNonDeductiblePermanentDifferences" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_EffectiveIncomeTaxRateReconciliationNonDeductiblePermanentDifferences" xlink:to="bgm_EffectiveIncomeTaxRateReconciliationNonDeductiblePermanentDifferences_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_EffectiveIncomeTaxRateReconciliationNonDeductiblePermanentDifferences_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of the difference between the effective income tax rate and the domestic federal statutory income tax rate attributable to permanent differences.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_EffectiveIncomeTaxRateReconciliationNonDeductiblePermanentDifferences_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective Income Tax Rate Reconciliation Non Deductible Permanent Differences</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_EffectiveIncomeTaxRateReconciliationNonDeductiblePermanentDifferences_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Permanent difference</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperations" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:to="us-gaap_EffectiveIncomeTaxRateContinuingOperations_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective Income Tax Rate Reconciliation, Percent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperations_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Effective tax rate</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SalesAndExciseTaxPayableCurrent" xlink:label="us-gaap_SalesAndExciseTaxPayableCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_SalesAndExciseTaxPayableCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">VAT tax payable</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccruedIncomeTaxesCurrent" xlink:label="us-gaap_AccruedIncomeTaxesCurrent" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AccruedIncomeTaxesCurrent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Corporate income tax payable</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_AffiliatedEntityMember" xlink:to="srt_AffiliatedEntityMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_RelatedPartyTransactionLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Related Party Transaction [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RelatedPartyTransactionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">RELATED PARTY TRANSACTIONS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax" xlink:label="us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax" xlink:to="us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Revenue from Contract with Customer, Including Assessed Tax</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RevenueFromContractWithCustomerIncludingAssessedTax_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sales to affiliated companies</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseExpense" xlink:label="us-gaap_OperatingLeaseExpense" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseExpense" xlink:to="us-gaap_OperatingLeaseExpense_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease, Expense</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseExpense_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating lease expenses</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsAndLiabilitiesLesseeAbstract" xlink:label="us-gaap_AssetsAndLiabilitiesLesseeAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsAndLiabilitiesLesseeAbstract" xlink:to="us-gaap_AssetsAndLiabilitiesLesseeAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetsAndLiabilitiesLesseeAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Assets and Liabilities, Lessee [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AssetsAndLiabilitiesLesseeAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease Assets:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilityAbstract" xlink:label="us-gaap_OperatingLeaseLiabilityAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseLiabilityAbstract" xlink:to="us-gaap_OperatingLeaseLiabilityAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseLiabilityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease, Liability [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseLiabilityAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating lease obligations:</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiability" xlink:label="us-gaap_OperatingLeaseLiability" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseLiability" xlink:to="us-gaap_OperatingLeaseLiability_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease, Liability</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total Lease liabilities</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:label="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:to="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease, Weighted Average Remaining Lease Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Remaining Lease Term Operating Lease</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:label="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:to="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Operating Lease, Weighted Average Discount Rate, Percent</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Discount rate</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:label="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract" xlink:to="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, Payment, Due [Abstract]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">LEASE</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid, Year One</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid, Year Two</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, to be Paid</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Total minimum lease payments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Lessee, Operating Lease, Liability, Undiscounted Excess Amount</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Less: Imputed interest</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfStockByClassTable" xlink:label="us-gaap_ScheduleOfStockByClassTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfStockByClassTable" xlink:to="us-gaap_ScheduleOfStockByClassTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfStockByClassTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Stock by Class [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PlanNameAxis" xlink:label="us-gaap_PlanNameAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PlanNameAxis" xlink:to="us-gaap_PlanNameAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PlanNameAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Plan Name [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PlanNameDomain" xlink:label="us-gaap_PlanNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PlanNameDomain" xlink:to="us-gaap_PlanNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PlanNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Plan Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_EquityIncentivePlan2024Member" xlink:label="bgm_EquityIncentivePlan2024Member" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_EquityIncentivePlan2024Member" xlink:to="bgm_EquityIncentivePlan2024Member_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_EquityIncentivePlan2024Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Representing member information pertaining to 2024 equity incentive plan.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_EquityIncentivePlan2024Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Equity Incentive Plan 2024 [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_EquityIncentivePlan2024Member_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2024 Equity Incentive Plan</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_AiSolutionsAndInsuranceBusinessMember" xlink:label="bgm_AiSolutionsAndInsuranceBusinessMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_AiSolutionsAndInsuranceBusinessMember" xlink:to="bgm_AiSolutionsAndInsuranceBusinessMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_AiSolutionsAndInsuranceBusinessMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to AI Solutions and Insurance Business.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_AiSolutionsAndInsuranceBusinessMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">AI Solutions And Insurance Business [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_AiSolutionsAndInsuranceBusinessMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">AI Solutions and Insurance Business</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_ZhijiuHoldingsLimitedMember" xlink:label="bgm_ZhijiuHoldingsLimitedMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_ZhijiuHoldingsLimitedMember" xlink:to="bgm_ZhijiuHoldingsLimitedMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_ZhijiuHoldingsLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the information pertaining to Zhijiu Holdings Limited.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_ZhijiuHoldingsLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Zhijiu Holdings Limited [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_ZhijiuHoldingsLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Zhijiu Holdings Limited</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsidiarySaleOfStockAxis" xlink:label="us-gaap_SubsidiarySaleOfStockAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsidiarySaleOfStockAxis" xlink:to="us-gaap_SubsidiarySaleOfStockAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Stock [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SaleOfStockNameOfTransactionDomain" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Stock [Domain]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IPOMember" xlink:label="us-gaap_IPOMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IPOMember" xlink:to="us-gaap_IPOMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IPOMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">IPO</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IPOMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">IPO</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfStockLineItems" xlink:label="us-gaap_ClassOfStockLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ClassOfStockLineItems" xlink:to="us-gaap_ClassOfStockLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ClassOfStockLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class of Stock [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ClassOfStockLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class of Stock</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_AuthorizedCapital" xlink:label="bgm_AuthorizedCapital" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_AuthorizedCapital" xlink:to="bgm_AuthorizedCapital_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_AuthorizedCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The amount of authorized capital.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_AuthorizedCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Authorized Capital</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_AuthorizedCapital_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Authorized Capital</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xlink:to="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class of Warrant or Right, Number of Securities Called by Each Warrant or Right</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of warrants issued</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_PercentageOfNumberOfOrdinarySharesSoldInIpo" xlink:label="bgm_PercentageOfNumberOfOrdinarySharesSoldInIpo" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_PercentageOfNumberOfOrdinarySharesSoldInIpo" xlink:to="bgm_PercentageOfNumberOfOrdinarySharesSoldInIpo_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_PercentageOfNumberOfOrdinarySharesSoldInIpo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The percentage of number of ordinary shares sold in IPO.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_PercentageOfNumberOfOrdinarySharesSoldInIpo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of Number of Ordinary Shares Sold In IPO</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_PercentageOfNumberOfOrdinarySharesSoldInIpo_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of number of ordinary shares sold in IPO</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_WarrantTerm" xlink:label="bgm_WarrantTerm" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_WarrantTerm" xlink:to="bgm_WarrantTerm_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_WarrantTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Period of warrants term, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_WarrantTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Warrant Term</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_WarrantTerm_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Warrant term</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:label="us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:to="us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class of Warrant or Right, Exercise Price of Warrants or Rights</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Exercise price (in dollars per share)</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_PercentageOfWarrantsExercisePriceBasedOnIpoIssuePrice" xlink:label="bgm_PercentageOfWarrantsExercisePriceBasedOnIpoIssuePrice" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_PercentageOfWarrantsExercisePriceBasedOnIpoIssuePrice" xlink:to="bgm_PercentageOfWarrantsExercisePriceBasedOnIpoIssuePrice_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_PercentageOfWarrantsExercisePriceBasedOnIpoIssuePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents the percentage of warrants exercise Price based on IPO issue price.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_PercentageOfWarrantsExercisePriceBasedOnIpoIssuePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of Warrants Exercise Price Based On IPO Issue Price</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_PercentageOfWarrantsExercisePriceBasedOnIpoIssuePrice_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of warrants exercise price based on IPO issue price</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SaleOfStockPricePerShare" xlink:label="us-gaap_SaleOfStockPricePerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SaleOfStockPricePerShare" xlink:to="us-gaap_SaleOfStockPricePerShare_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SaleOfStockPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Sale of Stock, Price Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SaleOfStockPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Share issue price</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfWarrantOrRightOutstanding" xlink:label="us-gaap_ClassOfWarrantOrRightOutstanding" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ClassOfWarrantOrRightOutstanding" xlink:to="us-gaap_ClassOfWarrantOrRightOutstanding_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ClassOfWarrantOrRightOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class of Warrant or Right, Outstanding</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ClassOfWarrantOrRightOutstanding_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Warrants outstanding</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_ClassOfWarrantOrRightsExercised" xlink:label="bgm_ClassOfWarrantOrRightsExercised" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_ClassOfWarrantOrRightsExercised" xlink:to="bgm_ClassOfWarrantOrRightsExercised_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_ClassOfWarrantOrRightsExercised_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of warrants or rights exercised as on date.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_ClassOfWarrantOrRightsExercised_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class of Warrant or Rights, Exercised</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_ClassOfWarrantOrRightsExercised_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of warrants or rights exercised as on date</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_MinimumPercentageOfReserveOfRegisteredCapitalForStatutorySurplusReserve" xlink:label="bgm_MinimumPercentageOfReserveOfRegisteredCapitalForStatutorySurplusReserve" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_MinimumPercentageOfReserveOfRegisteredCapitalForStatutorySurplusReserve" xlink:to="bgm_MinimumPercentageOfReserveOfRegisteredCapitalForStatutorySurplusReserve_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_MinimumPercentageOfReserveOfRegisteredCapitalForStatutorySurplusReserve_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The percentage of minimum percentage of reserve of registered capital for statutory surplus reserve.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_MinimumPercentageOfReserveOfRegisteredCapitalForStatutorySurplusReserve_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Minimum Percentage of Reserve of Registered Capital for Statutory Surplus Reserve</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_MinimumPercentageOfReserveOfRegisteredCapitalForStatutorySurplusReserve_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of reserve of registered capital for statutory surplus reserve</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_PercentageOfStatutorySurplusReserve" xlink:label="bgm_PercentageOfStatutorySurplusReserve" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_PercentageOfStatutorySurplusReserve" xlink:to="bgm_PercentageOfStatutorySurplusReserve_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_PercentageOfStatutorySurplusReserve_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The percentage of statutory surplus reserve .</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_PercentageOfStatutorySurplusReserve_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage Of Statutory Surplus Reserve</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_PercentageOfStatutorySurplusReserve_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of statutory surplus reserve</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:label="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:to="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares Issued, Shares, Share-Based Payment Arrangement, after Forfeiture</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ordinary shares, granted</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharesIssuedPricePerShare" xlink:label="us-gaap_SharesIssuedPricePerShare" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharesIssuedPricePerShare" xlink:to="us-gaap_SharesIssuedPricePerShare_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SharesIssuedPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Shares Issued, Price Per Share</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SharesIssuedPricePerShare_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Purchase price per share</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:to="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Segment Reporting Information, by Segment [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementBusinessSegmentsAxis" xlink:label="us-gaap_StatementBusinessSegmentsAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementBusinessSegmentsAxis" xlink:to="us-gaap_StatementBusinessSegmentsAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementBusinessSegmentsAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segments [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain" xlink:label="us-gaap_SegmentDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentDomain" xlink:to="us-gaap_SegmentDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segments [Domain]</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_InternationalMarketsMember" xlink:label="bgm_InternationalMarketsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_InternationalMarketsMember" xlink:to="bgm_InternationalMarketsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_InternationalMarketsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">This member stands for international markets.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_InternationalMarketsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">International Markets [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_InternationalMarketsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">International markets</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_DiversifiedPharmaceuticalAndAlliedProductsMember" xlink:label="bgm_DiversifiedPharmaceuticalAndAlliedProductsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_DiversifiedPharmaceuticalAndAlliedProductsMember" xlink:to="bgm_DiversifiedPharmaceuticalAndAlliedProductsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_DiversifiedPharmaceuticalAndAlliedProductsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Representing member information pertaining to Diversified Pharmaceutical and Allied Products.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_DiversifiedPharmaceuticalAndAlliedProductsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Diversified Pharmaceutical and Allied Products [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_DiversifiedPharmaceuticalAndAlliedProductsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Diversified Pharmaceutical and Allied Products</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_AiSolutionsMember" xlink:label="bgm_AiSolutionsMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_AiSolutionsMember" xlink:to="bgm_AiSolutionsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_AiSolutionsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Representing member information pertaining to AI Solutions.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_AiSolutionsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">AI Solutions [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_AiSolutionsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">AI Solutions</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_InsuranceBusinessMember" xlink:label="bgm_InsuranceBusinessMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_InsuranceBusinessMember" xlink:to="bgm_InsuranceBusinessMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_InsuranceBusinessMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Representing member information pertaining to Insurance Business.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_InsuranceBusinessMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Insurance Business [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_InsuranceBusinessMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Insurance Business</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingInformationLineItems" xlink:label="us-gaap_SegmentReportingInformationLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentReportingInformationLineItems" xlink:to="us-gaap_SegmentReportingInformationLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentReportingInformationLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Segment Reporting Information [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SegmentReportingInformationLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SEGMENT REPORTING</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfOperatingSegments" xlink:label="us-gaap_NumberOfOperatingSegments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NumberOfOperatingSegments" xlink:to="us-gaap_NumberOfOperatingSegments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Operating Segments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of operating segments</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfReportableSegments" xlink:label="us-gaap_NumberOfReportableSegments" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NumberOfReportableSegments" xlink:to="us-gaap_NumberOfReportableSegments_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of Reportable Segments</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of reportable segments</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_DepreciationAndAmortizationExcludingAmortizationOfRightOfUseAssets" xlink:label="bgm_DepreciationAndAmortizationExcludingAmortizationOfRightOfUseAssets" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_DepreciationAndAmortizationExcludingAmortizationOfRightOfUseAssets" xlink:to="bgm_DepreciationAndAmortizationExcludingAmortizationOfRightOfUseAssets_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_DepreciationAndAmortizationExcludingAmortizationOfRightOfUseAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The aggregate expense recognized in the current period that allocates the cost of tangible assets, intangible assets, or depleting assets to periods that benefit from use of the assets excluding amortization on right-of-use assets.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_DepreciationAndAmortizationExcludingAmortizationOfRightOfUseAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Depreciation And Amortization Excluding Amortization Of Right-Of-Use Assets</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bgm_DepreciationAndAmortizationExcludingAmortizationOfRightOfUseAssets_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Depreciation and amortization</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_CapitalExpenditures" xlink:label="bgm_CapitalExpenditures" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_CapitalExpenditures" xlink:to="bgm_CapitalExpenditures_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_CapitalExpenditures_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount of capital expenditures incurred for purchase of property, plant and equipment.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_CapitalExpenditures_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capital Expenditures</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_CapitalExpenditures_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Capital expenditures</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:to="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Schedule of Business Acquisitions, by Acquisition [Table]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_CounterpartyNameAxis" xlink:label="srt_CounterpartyNameAxis" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_CounterpartyNameAxis" xlink:to="srt_CounterpartyNameAxis_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_CounterpartyNameAxis_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Counterparty Name [Axis]</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RepurchaseAgreementCounterpartyNameDomain" xlink:label="srt_RepurchaseAgreementCounterpartyNameDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RepurchaseAgreementCounterpartyNameDomain" xlink:to="srt_RepurchaseAgreementCounterpartyNameDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RepurchaseAgreementCounterpartyNameDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Counterparty Name [Domain]</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_AhanzhaiDevelopmentCoLtdMember" xlink:label="bgm_AhanzhaiDevelopmentCoLtdMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_AhanzhaiDevelopmentCoLtdMember" xlink:to="bgm_AhanzhaiDevelopmentCoLtdMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_AhanzhaiDevelopmentCoLtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Representing member information pertaining to Ahanzhai Development Co Ltd.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_AhanzhaiDevelopmentCoLtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ahanzhai Development Co. Ltd [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_AhanzhaiDevelopmentCoLtdMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Ahanzhai Development Co., Ltd.</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_LxManagementCompanyLimitedMember" xlink:label="bgm_LxManagementCompanyLimitedMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_LxManagementCompanyLimitedMember" xlink:to="bgm_LxManagementCompanyLimitedMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_LxManagementCompanyLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Representing member information pertaining to LX Management Company Limited.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_LxManagementCompanyLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">LX Management Company Limited [Member]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_LxManagementCompanyLimitedMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">LX Management Company Limited</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionLineItems" xlink:label="us-gaap_BusinessAcquisitionLineItems" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionLineItems" xlink:to="us-gaap_BusinessAcquisitionLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_BusinessAcquisitionLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">THE ACQUISITION OF THE Company of AI Solutions and Insurance Business, YX Management Company Limited, Yang Lou Dong, HM Management Company Limited</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:label="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:to="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Capital Shares Reserved for Future Issuance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Number of shares agreed to issue</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_BusinessAcquisitionPercentageOfVotingInterestsAgreedToAcquired" xlink:label="bgm_BusinessAcquisitionPercentageOfVotingInterestsAgreedToAcquired" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_BusinessAcquisitionPercentageOfVotingInterestsAgreedToAcquired" xlink:to="bgm_BusinessAcquisitionPercentageOfVotingInterestsAgreedToAcquired_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_BusinessAcquisitionPercentageOfVotingInterestsAgreedToAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Percentage of voting interest agreed to acquired.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_BusinessAcquisitionPercentageOfVotingInterestsAgreedToAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Acquisition Percentage Of Voting Interests Agreed To Acquired</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_BusinessAcquisitionPercentageOfVotingInterestsAgreedToAcquired_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Company agreed to acquired</label>
    <loc xlink:type="locator" xlink:href="bgm-20250930.xsd#bgm_CommonStockConsiderationForFutureIssuance" xlink:label="bgm_CommonStockConsiderationForFutureIssuance" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_CommonStockConsiderationForFutureIssuance" xlink:to="bgm_CommonStockConsiderationForFutureIssuance_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_CommonStockConsiderationForFutureIssuance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aggregate amount of consideration receivable for shares to be issued.</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bgm_CommonStockConsiderationForFutureIssuance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Common Stock, Consideration For Future Issuance</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bgm_CommonStockConsiderationForFutureIssuance_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Consideration</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:to="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Proceeds from Issuance of Common Stock</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Amount received</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:to="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Business Combination, Consideration Transferred, Equity Interests Issued and Issuable</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">The value of the shares issued</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherCommitmentsDomain" xlink:to="us-gaap_OtherCommitmentsDomain_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherCommitmentsDomain_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Commitments [Domain]</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bgm_OperatingLeaseCommitmentsMember" xlink:to="bgm_OperatingLeaseCommitmentsMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_OperatingLeaseCommitmentsMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to operating lease commitments.</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bgm_CapitalCommitmentMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Represents information pertaining to capital commitment.</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherCommitmentsLineItems" xlink:to="us-gaap_OtherCommitmentsLineItems_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherCommitmentsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Other Commitments [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherCommitmentsLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">COMMITMENTS</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractualObligation" xlink:label="us-gaap_ContractualObligation" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ContractualObligation" xlink:to="us-gaap_ContractualObligation_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ContractualObligation_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contractual Obligation</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractualObligationDueInNextTwelveMonths" xlink:label="us-gaap_ContractualObligationDueInNextTwelveMonths" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ContractualObligationDueInNextTwelveMonths" xlink:to="us-gaap_ContractualObligationDueInNextTwelveMonths_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ContractualObligationDueInNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contractual Obligation, to be Paid, Year One</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ContractualObligationDueInNextTwelveMonths_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2026</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractualObligationDueInSecondYear" xlink:label="us-gaap_ContractualObligationDueInSecondYear" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ContractualObligationDueInSecondYear" xlink:to="us-gaap_ContractualObligationDueInSecondYear_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ContractualObligationDueInSecondYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Contractual Obligation, to be Paid, Year Two</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ContractualObligationDueInSecondYear_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">2027</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventTable" xlink:to="us-gaap_SubsequentEventTable_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventTable_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Event [Table]</label>
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTypeDomain" xlink:label="us-gaap_SubsequentEventTypeDomain" xmlns="http://www.xbrl.org/2003/linkbase" />
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    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventMember" xlink:label="us-gaap_SubsequentEventMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventMember" xlink:to="us-gaap_SubsequentEventMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent events</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SubsequentEventMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent events</label>
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PrivatePlacementMember" xlink:label="us-gaap_PrivatePlacementMember" xmlns="http://www.xbrl.org/2003/linkbase" />
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PrivatePlacementMember" xlink:to="us-gaap_PrivatePlacementMember_lbl" xmlns="http://www.xbrl.org/2003/linkbase" />
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PrivatePlacementMember_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Private Placement [Member]</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Subsequent Event [Line Items]</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SubsequentEventLineItems_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">SUBSEQUENT EVENTS</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Class of Warrant or Right, Number of Securities Called by Warrants or Rights</label>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights_lbl" xml:lang="en-US" xmlns="http://www.xbrl.org/2003/linkbase">Aggregate class A ordinary shares underlying warrants</label>
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