Hi Debby!
Thank you for bringing your question to the Disney Parks Moms Panel!
You have the right idea in that the bus from
Magic Kingdom Park to
Disney's Animal Kingdom Lodge would be the best (free) way to travel there from
Disney's Contemporary Resort. You can walk to the Magic Kingdom, take the
monorail or take a ferryboat to get there. Walking is the quickest way and there is a pathway for you to follow. I think you can walk to the bus stop in about ten minutes. I would allow about one and a half hours to be sure to get there on time. The buses from Magic Kingdom to Animal Kingdom Lodge will begin running one hour prior to when Magic Kingdom opens, so they should be going when you need them.
Another option to consider is using the
Minnie Van Service. These vans can be scheduled using the Lyft app and will take you straight from the Contemporary Resort to Animal Kingdom Lodge. Minnie Vans are a flat rate of $25. Using a taxi, Uber or regular Lyft would also work and would probably be a bit cheaper than the Minnie Vans. However, the Minnie Vans do come with two child seats if that is an issue for you.
I hope this information is helpful! Please let me know if you have any other questions as you plan for your trip.