Fair Value Measurements - Narrative (Details) - USD ($)	3 Months Ended
Dec. 31, 2021	Dec. 31, 2020	Sep. 30, 2021
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Impairment of projects in process	$ 0	$ 0
Impairment charges on land held for sale	0	$ 0
Level 2 \| Fair Value, Measurements, Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Deferred compensation plan assets	$ 3,000,000		$ 2,700,000

Deferred Compensation Plan Assets, Fair Value Disclosure

No definition available.

Name:	bzh_DeferredCompensationPlanAssetsFairValueDisclosure
Namespace Prefix:	bzh_
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_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

The aggregate amount of write-downs for impairments recognized during the period for long-lived assets held for abandonment, exchange or sale.

+ References

Reference 1: 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=123570139&loc=d3e3602-108585

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 360
-SubTopic 10
-Section 45
-Paragraph 15
-URI http://asc.fasb.org/extlink&oid=123351718&loc=d3e2611-110228

+ Details

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

- Definition

Amount recognized as an operating expense or loss during the period to reduce the carrying amount of a project that has been impaired but not abandoned.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 360
-SubTopic 10
-Section 45
-Paragraph 4
-URI http://asc.fasb.org/extlink&oid=123351718&loc=d3e2420-110228

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=123570139&loc=d3e3602-108585

+ Details

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

- Details

Name:	us-gaap_FairValueByFairValueHierarchyLevelAxis=us-gaap_FairValueInputsLevel2Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

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