How can I keep my branch up to date with master with git?

If you just want the bug fix to be integrated into the branch, git cherry-pick the relevant commit(s).

If your branch is local only and hasn't been pushed to the server, use

git rebase master

Otherwise, use

git merge master

Assuming you're fine with taking all of the changes in master, what you want is:

git checkout <my branch>

to switch the working tree to your branch; then:

git merge master

to merge all the changes in master with yours.

You can use the cherry-pick to get the particular bug fix commit(s)

$ git checkout branch
$ git cherry-pick bugfix