Just call Mears at 407-423-5566. Tell them the date you want the shuttle and they will give you a list of available times. Reserve the times you want and they'll give you a confirmation number for each way. Better to reserve now because sometimes the earlier times fill up in advance. You don't have to pay ahead, you just give the driver cash when you board. If you are at the park and you find you want to leave earlier than your scheduled time, just call them and they can put you on the next available return shuttle.
We use them quite a bit for clients who stay onsite at Disney and don't rent a car.