ME only runs between the airport and the resorts.
You can take the regular bus. If you do, you'll need to be at the bus stop by 7:00.
You can also take a cab to MK, but I think they actually drop off at the TTC, so you'll still need to take the monorail or the ferry to the park. You could also take a cab to the Contemporary and walk to MK. Either way, I would leave the hotel by 7:15.
Between the two, I would just take the bus.