Hi Kristen!
Thank you for visiting the Moms Panel!
Chef Mickey's is a wonderful choice for a birthday celebration.
I would recommend taking a bus to the Magic Kingdom park, and then transfer to the monorail for Disney's Contemporary Resort. The Disney Transportation starts operating approximately one hour before theme park opening, so the buses at Disney's Art of Animation Resort would usually begin arriving around 8.00 a.m., unless the Magic Kingdom is operating Extra Magic Hours on that morning, when the park will open at 8.00 a.m., and the buses will arrive from 7.00 a.m. (Check the
Magic Kingdom park calendar for the day of your visit, to see what time it opens that day.) The total travelling time for this route would be approximately 40 minutes, but please remember to include extra time waiting for transport and walking to/from the bus/monorail stops. Generally it is suggested to allow 60-90 minutes when travelling between resorts.
There is also a special bus service from resorts for those with early character dining reservations. Please check with your front desk about this service - for times and where to wait for this bus.
If you have any other questions, please come back and ask me - I would be happy to help you plan your magical vacation!