From Disney's Animal Kingdom theme Park to Disney Springs you can use the bus system but a transfer at a resort is required.
If you go first to Saratoga Springs (Congress Park stop) the second leg of the journey can optionally be done on foot (no pun intended). You'd be entering DS at the Marketplace (north) end.
If you go first to Port Orleans (either) you can optionally take a boat the rest of the way.
Or you might just take the first resort bus that comes (excluding Contemporary, Grand Floridian, Polynesian or the Wilderness's, where the total travel distance is much greater).
There are NO buses that to to DS from ANY Park, to discourage people parking at DSfor free when going to the parks. The closest resort to AK is AKL. You can take the bus to that resort and then catch their DS bus. Or follow Seashore CM's suggestions.