In Bamboo if you build customized there is a field named "Revision" where you can define which commit is checket out (sha commit id). This field is missing in JIRAs "Build & Release".
I was looking for this feature too, and I couldn't find it either, so I made a Improvement request[1]. If you're interested, please feel free to comment and vote for it. [1]: https://jira.atlassian.com/browse/JRA-43648
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