It depends on the route your bus takes. Typical morning routing would be Swan -> Dolphin -> Boardwalk. That can change as needed. Assuming the bus takes that route above, it'll probably be 17 minutes to the Magic Kingdom, give or take, plus wait time for the bus. Average total time, half hour, give or take.
If you drive, remember that you have to park at the TTC. Even though you may park for free, you still have to wait in line at the Toll Plaza. Then, you have to park your car, and either walk under the bridge, or take the tram. After that, you'll need to take the Ferry or Monorail over. Average total time, about 45 minutes, give or take.
It should be noted that guests at the TTC are held back until 8:45 on most mornings. Resort buses go directly to the MK front gates.