But I'd allow at least an hour from the time you get to the bus stop at DTD. Most of those buses aren't direct buses. The one I got on (Grand Floridian Stop) the last time I did this went to WL, Fort Wilderness (I think), then the Grand Floridian. It took quite a while.
A different option would be to go to one of the buses that is a direct bus fairly close to DTD (like Port Orleans, OKW, or Saratoga Springs) then switch to the MK bus.
And finally, there is always the option to take a taxi. If I was running short on time, it would be worth the money to me.