Note 5 - Fair Value Measurements (Details Textual) - USD ($) $ in Thousands	3 Months Ended
Dec. 31, 2020	Sep. 30, 2019	Dec. 31, 2019
Long-term Debt, Fair Value	$ 118,400		$ 146,400
Long-term Debt, Gross	115,600		143,700
Goodwill, Impairment Loss	0
Goodwill, Ending Balance	23,966	$ 10,800	21,993
North America Reporting Unit [Member]
Goodwill, Impairment Loss		8,900
Goodwill, Impairment Loss, Net of Tax		$ 8,500
Fair Value, Nonrecurring [Member]
Assets, Fair Value Disclosure	0		0
Foreign Exchange Forward [Member]
Derivative Asset, Total	100
Investments Held in Rabbi Trust [Member]
Debt Securities, Available-for-sale, Total	$ 700		$ 1,100

Fair value portion of probable future economic benefits obtained or controlled by an entity as a result of past transactions or events.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=117815213&loc=d3e19207-110258

+ Details

Name:	us-gaap_AssetsFairValueDisclosure
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(6))
-URI http://asc.fasb.org/extlink&oid=120398452&loc=d3e534808-122878

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 30
-Section 45
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=121558606&loc=SL82898722-210454

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 45
-Paragraph 1
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=121553693&loc=d3e26610-111562

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (aa)
-URI http://asc.fasb.org/extlink&oid=121645371&loc=d3e27161-111563

+ Details

Name:	us-gaap_AvailableForSaleSecuritiesDebtSecurities
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount, before unamortized (discount) premium and debt issuance costs, of long-term debt. Includes, but is not limited to, notes payable, bonds payable, commercial loans, mortgage loans, convertible debt, subordinated debt and other types of debt.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 4
-Subparagraph (b)(1)
-URI http://asc.fasb.org/extlink&oid=120520924&loc=SL6031897-161870

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(16))
-URI http://asc.fasb.org/extlink&oid=120400017&loc=d3e572229-122910

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(22))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(16))
-URI http://asc.fasb.org/extlink&oid=120398452&loc=d3e534808-122878

+ Details

Name:	us-gaap_DebtInstrumentCarryingAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Fair value, after the effects of master netting arrangements, of a financial asset or other contract with one or more underlyings, notional amount or payment provision or both, and the contract can be net settled by means outside the contract or delivery of an asset. Includes assets not subject to a master netting arrangement and not elected to be offset.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 55
-Paragraph 10
-URI http://asc.fasb.org/extlink&oid=99393222&loc=SL20226008-175313

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 825
-SubTopic 10
-Section 50
-Paragraph 10
-URI http://asc.fasb.org/extlink&oid=121572278&loc=d3e13433-108611

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 50
-Paragraph 3
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=51824906&loc=SL20225862-175312

+ Details

Name:	us-gaap_DerivativeAssets
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount after accumulated impairment loss of an asset representing future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(10)(1))
-URI http://asc.fasb.org/extlink&oid=120398452&loc=d3e534808-122878

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 20
-Section 45
-Paragraph 5
-URI http://asc.fasb.org/extlink&oid=120320667&loc=SL49117168-202975

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 20
-Section 45
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=99380562&loc=d3e13770-109266

+ Details

Name:	us-gaap_Goodwill
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of loss from the write-down of an asset representing the future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 20
-Section 50
-Paragraph 2
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=121556970&loc=d3e13854-109267

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 28
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=121586364&loc=d3e3602-108585

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 20
-Section 50
-Paragraph 1
-Subparagraph (e)
-URI http://asc.fasb.org/extlink&oid=121556970&loc=d3e13816-109267

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 20
-Section 45
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=99380562&loc=d3e13777-109266

+ Details

Name:	us-gaap_GoodwillImpairmentLoss
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount after tax of loss recognized that results from the write-down of an asset representing the future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized.

+ References

No definition available.

+ Details

Name:	us-gaap_GoodwillImpairmentLossNetOfTax
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

The fair value amount of long-term debt whether such amount is presented as a separate caption or as a parenthetical disclosure. Additionally, this element may be used in connection with the fair value disclosures required in the footnote disclosures to the financial statements. The element may be used in both the balance sheet and disclosure in the same submission.

+ References

No definition available.

+ Details

Name:	us-gaap_LongTermDebtFairValue
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Details

Name:	us-gaap_ReportingUnitAxis=belfa_NorthAmericaReportingUnitMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FairValueByMeasurementFrequencyAxis=us-gaap_FairValueMeasurementsNonrecurringMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=us-gaap_ForeignExchangeForwardMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=belfa_InvestmentsHeldInRabbiTrustMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: