I would allow at least an hour.
Take your resort bus to Magic Kindgom & walk to the Contemporary from the MK bus depot. Don't be tempted to take the Monorail! I have had to wait on the Monorail *waiting* for the "next station to clear" quite a few times. It can be very frustrating when you're trying to get to an ADR on time.
Catch a taxi at ASMu. It'll be about $10 or $15, but will probably be less stressful if you're running late.
agnes!