As the PP said, there are no direct buses from any of the theme parks to DTD (or vice-a-versa). They did try an afternoon bus from AK to DTD, but that trial ended last fall and has not been re-started anywhere else.
There are a couple of different options if you want to stick to using Disney transportation. I would
budget between 60-90 minutes because they all involve a transfer of some sort.
1) Take the boat or walk to one of the Epcot resorts and then catch a bus to DTD.
2) Take a bus to Old Key West or Saratoga Springs, Port Orleans Riverside, or Port Orleans French Quarter and then take the boat to DTD.
3) Take the bus to Saratoga Springs and then walk to DTD.
In truth, you could take any resort bus from DTD and then transfer to a DTD bus at that resort. If you go that route, I would avoid any resort that takes you further away from DTD (e.g., AKL, All Stars, etc.).
Personally, I would probably spring for the taxi. It'll be about $20 (plus tip) and takes about 20 minutes.