You can go directly from every theme park to every other theme park (as long as you include the Transportation & Ticket Center as part of Magic Kingdom).
There is a DIRECT bus between Animal Kingdom and Disney's Hollywood Studios.
There is a DIRECT bus between Animal Kingdom and Epcot.
There is a DIRECT bus between Animal Kingdom and the TTC (and to/from there you take a monorail or ferry to/from Magic Kingdom).
There is a DIRECT bus between DHS and Epcot. You can also take a FriendShip boat from one to the other. You can also walk from one to the other.
There is a DIRECT bus between DHS and the TTC (and to/from there you take a monorail or ferry to/from Magic Kingdom)
To go from either AK or DHS to MK, your other choice is to take a bus to Contemporary, and then take the short walk from Contemporary to MK.
There is NO BUS between MK and Epcot ... from MK, you need to get to TTC (by monorail or ferry) and then from TTC you'd take the monorail to Epcot.
I think that covers all of the basic inter-park routes. You NEVER have to use a resort as a transportation hub to go from one theme park to another.