When I follow my bookmark to our Bitbucket server, I am redirected to cas for single sign on (SSO), and after authenticating I can browse our projects and repositories.
After installing Sourcetree I try to 'register'. I enter the URL for our Bitbucket server and my user name, then click Login and enter my password. I'm sent back to the login screen of the installer with this error message in red:
Failed to check login for user [...] : You do not have permission to access URL 'https://bitbucket.../rest/api/1.0/users/...' please check the user credentials associated with this account. The request returned with status code 'Unauthorized'.
How can I set up Sourcetree to work with our Bitbucket server and SSO?
This isn't particular to Sourcetree but to how your admin configured the Bitbucket Server instance. If Sourcetree can't load your user profile, as noted by that message, then registration is broken. I'd recommend contacting them to find out why and get that lifted if possible.
Principal Developer, Sourcetree