Last October, several of my family wanted to go from Epcot to Downtown Disney (we were staying at OKW and did not want to go back there and then go to Downtown Disney). We walked to Boardwalk and took the bus from there. When we got to the bus stop, there was a group waiting who had a person using a wheelchair. They told us that the last Downtown Disney bus had been there about 15 minutes before had been too full for them to get on. When the next bus arrived, it was also too full, so they were still waiting for the bus when we left.
You would be able to easily get to Epcot and the Studio with either the boat or the walking paths. You could also get to MK by going thru Epcot and using the monorail if you want to avoid the buses to go there. You could also check with the resort to find out which resort is the first stop for where you are going and then go to the bus stop for that resort - that should help you to get on the bus with the least difficulty.