A Bitbucket repository which is owned by an individual account can't be used with Jenkins as the Branch Source Plugin Currently functions.
Currently, when loading the repositories after entering the Owner name, It makes a request to the BB API essentially "Give me all projects the credentialed user is a teammember on, or all repos owned by the crednetialed user, which are also owned by the username above".
This causes a gap in the repo you're attempting to build is not a part of a project that your jenkins account is a team-member on, but instead is just a contributor for on someone else's repo.
In Version 2.1.x the repository name was just a text field, allowing you to enter owner and repo manually and it worked fine. My Jenkins is now stuck at that version (and the related old versions of other plugins) because it can't properly select our repo anymore.