Performing any operation on a Bitbucket repo using SourceTree causes errors.

Upon performing any action requiring a connection to the remote (pull, push, etc.) login prompts appear over and over and never stop.  I have an app password for Sourcetree and that doesn't work. My main Bitbucket password also doesn't work. Additionally I have an SSH key set up on both Bitbucket and the computer where I'm running SourceTree.

This is not the first time I've experienced this.  Getting SourceTree to properly authenticate with Bitbucket is like pulling teeth.  Before I remove this from my computer and replace it with something that actually works, I want to give this one last shot.

There's even a bug with the ticket reporting system. I'm running SourceTree 3.3.9 and it's telling me that version doesn't exist!