Owned Inventory - Total Owned Inventory by Segment (Details) - USD ($) $ in Thousands	Mar. 31, 2024	Sep. 30, 2023
Segment Reporting Information [Line Items]
Projects in progress	$ 2,019,318	$ 1,717,745
Land held for future development	19,879	19,879
Land held for sale	18,264	18,579
Total owned inventory	2,057,461	1,756,203
Corporate and unallocated
Segment Reporting Information [Line Items]
Projects in progress	200,086	180,300
Land held for future development	0	0
Land held for sale	0	0
Total owned inventory	200,086	180,300
West \| Operating Segments
Segment Reporting Information [Line Items]
Projects in progress	1,076,824	914,908
Land held for future development	3,483	3,483
Land held for sale	13,004	14,702
Total owned inventory	1,093,311	933,093
East \| Operating Segments
Segment Reporting Information [Line Items]
Projects in progress	392,848	325,395
Land held for future development	10,888	10,888
Land held for sale	4,584	3,201
Total owned inventory	408,320	339,484
Southeast \| Operating Segments
Segment Reporting Information [Line Items]
Projects in progress	349,560	297,142
Land held for future development	5,508	5,508
Land held for sale	676	676
Total owned inventory	$ 355,744	$ 303,326

Carrying amount as of the balance sheet date of project in progress

No definition available.

Name:	bzh_InventoryProjectsInProgress
Namespace Prefix:	bzh_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Carrying amount as of the balance sheet date of parcels of land held for sale, and on which the entity has no intention or no further intention to perform construction activities.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.6(a))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

+ Details

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

- Definition

The net carrying amount as of the balance sheet date of the sum of the various components of an operative builder's inventory, including finished homes. Operative builders primarily consist of entities that develop land, construct residential homes and commercial and industrial buildings thereon, and sell them to home buyers and operators of the commercial and industrial properties.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(6)(a))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

+ Details

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

- Definition

Carrying amount of land available for development.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 944
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(1)(d))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479440/944-210-S99-1

+ Details

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

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

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

- Details

Name:	srt_ConsolidationItemsAxis=us-gaap_CorporateNonSegmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_StatementBusinessSegmentsAxis=bzh_WestSegmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_ConsolidationItemsAxis=us-gaap_OperatingSegmentsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_StatementBusinessSegmentsAxis=bzh_EastSegmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_StatementBusinessSegmentsAxis=bzh_SoutheastSegmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: