There won't be a direct bus from the Animal Kingdom to the Magic Kingdom, however these would be your two options you can do when it comes to using the Disney buses.
1) Get on the Contemporary/Polynesian/Grand Floridian bus. Assuming it also goes to Blizzard Beach after it leaves from there the Contemporary will be the 1st stop among those resorts, so you can get off there and use the walkway to the Magic Kingdom.
2) Get on the bus directly to the Transportation & Ticket Center, then from there use the Express Monorail or boat when going to the Magic Kingdom.
Personally I would go with the 1st option if that bus is already there when you get to the bus station. However if the Contemporary bus is not there and the one for the TTC is, then I would get on that one.