The app supports an incremental mode to speed up the analysis of your pull requests by only passing the changed and new files of a pull request diff to Sonar instead of the complete project.
You just have to enable "incremental mode" by configuring for which branches it should be used in the Bamboo task as follows:
We also recommend that you enable creating plan branches for pull requests, because only with this mode a full analysis will be prevented when you push a new branch to Bitbucket Server and instead be deferred until the pull request is created: