In git a "branch" is literally a mapping between a name and the commit ID of the commit at the head of the branch. If you've merged your commit into the main development trunk (submitting the bugfix) there is essentially zero overhead to keeping the branch around in your repository.
Some CI systems have a mechanism where you create what you think will be the fix, then push it up to a common area for testing, review, etc. Then you respin your fix based on feedback, send it back in. Rinse, wash, repeat until everyone is satisfied, then merge for real. In that sort of environment it can be handy to have one local branch per bug that you're working on.
So one branch per bug you're working on, one branch per feature you're working on, one branch per released version, etc. I just checked and one local git repo I'm working on is sitting at around 40 local branches currently.