The Atlassian team provided a solution for this (here):
- Open the repo
- Click "Settings"
- Double click on the "origin" item in the listing
- Edit the url to add your username before the URL of the repo. Here are some examples:
https://USERNAME@contoso.com/repo/blah.git
https://USERNAME@github.com/host/repo_name
- You should be prompted for a password the next time you try to push or pull