Changing tmux .bash_profile behavior

tmux sets an environment variable called $TMUX, which I believe holds the location of the socket it's using. Either way you can use it in your .bash_profile to test whether or not it is being called from within tmux.

if [ -z "$TMUX" ]; then
    # not in tmux, do non-tmux things
fi

Or

if [ -n "$TMUX" ]; then
    # called inside tmux session, do tmux things
fi

I usually use $TERM to test that. screen and tmux set it to "screen" by default.