Operating Leases - Maturity Analysis of the Annual Undiscounted Cash Flows (Details) - USD ($) $ in Thousands	Dec. 31, 2020	Sep. 30, 2020
Lessee, Operating Lease, Liability, Payment, Due [Abstract]
2020	$ 3,364
2022	4,053
2023	3,254
2024	2,121
2025	1,824
Thereafter	3,000
Total lease payments	17,616
Less: Imputed interest	2,056
Total operating lease liabilities	$ 15,560	$ 15,333

Lessee, Operating Lease, Liability, to be Paid, after Year Four

No definition available.

Name:	bzh_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour
Namespace Prefix:	bzh_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 50
-Paragraph 6
-URI http://asc.fasb.org/extlink&oid=121609121&loc=SL77918701-209980

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease to be paid in next 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).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease to be paid in 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).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease to be paid in third 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).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease to be paid in second 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).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease having initial or remaining lease term in excess of one year to be paid in remainder of current fiscal year.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 50
-Paragraph 6
-URI http://asc.fasb.org/extlink&oid=121609121&loc=SL77918701-209980

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payments in excess of discounted obligation for lease payments for operating lease.

+ References

+ Details

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

- References

No definition available.

+ Details

Name:	us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Present value of lessee's discounted obligation for lease payments from operating lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 45
-Paragraph 1
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=121603541&loc=SL77918627-209977

+ Details

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