The git repo on github has a nice helper function for better tab completion for git. In case you type: git add TAB TAB you get a list of files that changed, or a new in your repo. If there is only one it will auto complete it. To install it copy the git-completion.bash to home folder, or use this code:
wget https://raw.github.com/git/git/master/contrib/completion/git-completion.bash \
-O ~/.git-completions.bash
To activate it and test if the completion works now as expected.
. ~/.git-completion.bash
To activate it automatically when you open a terminal.
echo ". ~/.git-completion.bash" >> "~/.bashrc"