While I can log in to the bitbucket server using a browser, and my SourceTree client on Windows 10 can authenticate with the bitbucket server, my SourceTree client on Mac Sierra cannot authenticate with the bitbucket server. I have a clone of a project on my Mac that SourceTree can see, but authentication fails when I attempt a pull. It pops up a dialog requiring my password - I enter the same password used for the browser login, but it pops up another dialog asking for the password. Eventually it gets to the point of telling me I have to log in with the browser and do a captcha - I successfully do that but after that SourceTree still cannot authenticate.
I have one suspicion - since the project was cloned on my Mac my network password has changed - this is the same password used by the bitbucket server. There appears to be no way to edit the password in SourceTree on Mac, although I was able to edit the password in the Windows SourceTree client and make this work.