At the moment you can allow Bitbucket Pipelines to make modifications to a repository by adding an SSH key inside Bitbucket Pipelines configuration and then adding the corresponding public key to the team access keys. The latter grants read-write access to every repository.
Could you add a simple checkbox to Bitbucket Pipelines to enable read-write access to the same repository? Upon enabling the access Bitbucket Pipelines should be allowed to push changes to the repository (assuming the image has git installed).
This enhancement would simplify configuration quite a bit.