We only used the Disney transportation to get to Magic Kingdom and then only because it was early entry and we couldn't drive. We drove everywhere else - Epcot, Typhoon Lagoon, Magic Kingdom, MGM, Downtown Disney, Boardwalk, and Wide World of Sports.
We never ran into any traffic or any problems parking - Disney is directing everything and you come in one way and leave another and the signage is pretty good. We went early, late, and in the afternoon throughut our stay and never had a problem and never waited for anything in terms of parking or getting to the front gate etc. Most of the time we were able to park within a block of the entrance and we just walked to and from our car. The only negative was a hot car. The only time we had a little trouble parking was when we went to Downtown Disney at about 8pm. We had to drive around for about five minutes before we found a spot. A minor minor problem.
It took less than fifteen minutes to get to AK, MGM, or Epcot. It was easy. Unless you really hate driving skip the Disney transportation.
P.S. I did see crabby people waiting for the bus, crowded busses that didn't stop, and people in standing in the street looking for the next bus to come.
Hope this helps.