Hi Jennifer!
Thank you for your great question. It sounds like your vacation will be full of magical moments! It's typically a good idea to allow an hour to get from your Disney Resort hotel to another location on Walt Disney World Resort property.
Because you will be taking a bus from Disney's Art of Animation Resort to Magic Kingdom park and then going to Disney's Contemporary Resort for your dinner at Chef Mickey's, I would suggest adding another 20-30 minutes to make sure you are there in time for your Advanced Dining Reservation.
Disney's Contemporary Resort is the first stop when you take the Resort Monorail from Magic Kingdom park, so that is definitely a convenient option for getting to the hotel.
Another idea is to walk. As you depart the bus stop at Magic Kingdom park, you'll see a dedicated path to the right of the Main Entrance that leads right to Disney's Contemporary Resort. It takes around 10 minutes to make the walk if you choose this option. Check out this
interactive map of Magic Kingdom park to get more details.
Enjoy your vacation and say "hi" to Mickey for me!