Adding
export EDITOR=vim
to your .bashrc should really do the trick. (There a no quotes necessary and, depending on what quotes you used, they may be the cause for your problem.)
You must open a new shell (or enter source ~/.bashrc
at the prompt) after modifying .bashrc for the modification to take effect.
What is the program from which you want vim to be started?
EDIT: I haven't used git, but the documentation (http://www.kernel.org/pub/software/scm/git/docs/git-commit.html) reads ``The editor used to edit the commit log message will be chosen from the GIT_EDITOR environment variable, the core.editor configuration variable, the VISUAL environment variable, or the EDITOR environment variable (in that order).''
So check whether one of these variables is set:
echo $GIT_EDITOR $VISUAL $EDITOR
git config --get-all core.editor
For me,
export VISUAL=vim
solved the problem.
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