I am not familiar with this plugin, but we quite successfully use Bitbucket and Jenkins together, however we poll for changes instead of having them pushed from BitBucket (due to the fact our build server is hidden behind a company firewall). This approach may work for you if you are still having problems with the current approach.
This document on Setting up SSH for Git & Mercurial on Linux covers the details of what you need to do to be able to communicate between your build server and Bitbucket over SSH. Once this is done, with the Git Plugin installed, go to your build configuration and select 'Git' under Source Code Management, and enter the ssh URL of your repository as the repository URL. Finally, in the Build Triggers section, select Poll SCM and set the poll frequency to whatever you require.