Not sure why you tagged the question as "bitbucket" and not "sourcetree". I fixed it, but at this point, it's too late for your question to show up in the inboxes of users who are subscribed to the Sourcetree tag.
It should be possible, so you probably haven't tried "everything".
Have you tried this? https://confluence.atlassian.com/bitbucket/how-do-i-use-ssh-with-sourcetree-282173660.html
If so, what went wrong?
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