Not sure how I didn't come across this earlier but it's a god send. Way easier to use long descriptive branch names once autocomplete is enabled!
Step 1) Download git-completion.bash from the git repo
# ~/.git-completion.bash
curl https://raw.github.com/git/git/master/contrib/completion/git-completion.bash \
-o ~/.git-completion.bash
Step 2) Add it to your .bash_profile
# ~/.bash_profile
if [ -f ~/.git-completion.bash ]; then
. ~/.git-completion.bash
fi
Open up a new terminal window or source ~/.bash_profile and you're good to go!