There doesn't seem to be a way to do so, but if you open a repository cloned elsewhere everything works just fine. It even prompts for your Bitbucket password if you try to push.

Yea, I was using Github for Mac previously, and all of my non-Github projects ported over to the Github Desktop app. Like the other reply said, you just have to manually clone and the 'Add' it.

You have to manually clone bitbucket stuff in. It supports that properly, with logins and all that. But you can't do it via the UI.