I've read Burke. ADG is excellent, though it would be even better if it had more concrete examples. It's also very much aimed at physicists (assuming advanced undergraduate knowledge of mechanics, E&M, etc.) and has less emphasis on mathematical rigor than most differential geometry texts.

I actually helped Burke out with a follow-up to ADG called Div, Grad, Curl are Dead, which looked very promising with lots of examples, but tragically he died from injuries sustained in a car accident before it could be polished for publication.