Further building on DaveEmme's answer here's what I finally put in my .bashrc to keep things simple:
case "$EMACS" in
t)
PROMPT_COMMAND=
PS1="[\u@\h:\w]$ "
esac
Relying on the value of $TERM didn't work in my case whereas Emacs is required to set the $EMACS environment variable to true for any shells it spawns.
