As a proof of concept, I was able to use the bitbucket status API to push build statuses to my team's repository.
I'm curious whether this is replicable or useful enough to branch it out into it's own reusable notifier, like the HTTP or Slack notifiers in this repo. I've read the code enough to feel comfortable taking a first crack at it if it seems useful, though I'm not sure how / where the docker images are stored for the built-in notifiers.