Judith,
Thanks for asking your question to planDisney!
To get from
Disney's Art of Animation Resort to
Disney's Contemporary Resort you basically take a bus from your resort to the
Magic Kingdom Park. That ride should take about 20 minutes, though of course you have to wait for the bus to arrive in the first place. After you arrive, you can simply walk over to the Contemporary, which is a quick 1/2 mile walk away. I would plan on about 40 minutes to an hour for the overall trip, just to be safe. It likely will take less time, but you always want to arrive in time for your reservation.
The buses from your resort to the Magic Kingdom will start running an hour before the park opening time. Normally that should be fine, but I would suggest you check that park opening time, to be certain that the buses will be running early enough to meet your reservation time. If your reservation is at 8:00 am, but the park opens at 9:00 am, you may not be able to rely on the bus to get you there on time. If that is the case, speak to your resort's front desk about what alternate solutions they can provide.
Write me back if you have any questions.
Have a Magical Vacation!
Doug