I don't remember exactly how long, but I would guess around 15-20 minutes. Buses start running an hour before opening. I would be at the bus stop about 7:45 to catch the first bus. At Epcot, I would go to the entrance marked for character breakfast entrance and tell them I'm there for an 8:30 segway tour. Last time, this entrance was on the far right.
It is possible that there might be an earlier bus. There might even be a character breakfast bus you can catch to Epcot.