You can enable an experimental feature to trigger GC automatically next time you accidentally push a large commit and go over the 2GB size limit.
Do this by clicking on your profile icon and selecting Labs, then enabling the feature "Delete dangling commits when over size limit". This only affects your personal login; tell your team in case they want to try it out too.
Next time you accidentally push large files to Bitbucket, follow the user guide to reset the branch to just before the large commit. When you force push that refs-only change, the Labs feature will automatically run GC to immediately remove the large commit.
This should bring your Bitbucket repo below the size limit, allowing you to push commits again without having to raise a support request. Anyone else using the same repo who has pulled the large commit will need to create a fresh clone.
Note that this won't work if your repo goes over 5GB. In that case your repo is put into read-only mode and you will need to request help from our support team at https://support.atlassian.com/contact/.