No, and not as far as I recall (although I could be wrong on the latter).
You can get buses directly outside the Magic Kingdom gates to the various resorts, or outside Epcot's front gates. But VERY few Disney buses go from the TTC to anywhere. And since the TTC is the outer entrance to MK, I'm 99% positive that no buses travel between it and Downtown Disney.
bus to Epcot (after Epcot closes and the monorail has shut down). This is for people who parked at Epcot in the morning an monorailed over to MK for evening EMH
In order to get a Bus to the Resorts use must take the Monorail or Ferryboat to the Magic Kingdom and change to the bus that goes to the resort you want to visit.
Also the outside Bus Companies drop off at the TTC Bus parking lot for the Magic Kingdom. Many guest like to catch the Lynx Bus from TTC to other attractions outside of Disney like Sea World for instance which would be route #50, there also a #56 route that goes out to Hwy 192, for more info on Lynx check there website.
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