The busses will generally start running an hour before the park's opening - including early entry times...so they'll get you there before the early entry gates open. The busses can get crowded, so if you decided to go busses, the best method would be to go to the Grandstand bus stop (if you're not staying in Grandstand, just walk over there). That will get you on the bus first before the other 4 stops.
Even though I drive to Disney, I really prefer to use transportation and not my car, to get to parks. Dealing with long lines streaming in, parking wherever they put me, then negotiating through Transportation Center to get to MK, and having to reverse the process to get back to my car, just doesn't feel all that convenient for me.
If truly desperate to shave all the minutes off that I can, I'd probably consider a Minnie Van to get there as they can drop off right at MK. Lyft is a lot cheaper, but will put you at TTC