I don't recommend the "bus from a park" approach. The bus system in the morning is designed to get guests *from* resorts, *to* parks. Hence they will often drop off at the parks, but not pick up, as they often will not even know at that point where they're headed next. You could find yourself waiting quite a while before a bus stops to pick up guests for any particular resort.
(Yes, I know this is counter-intuitive, but that's what happens.)
If you don't want to take Uber/Lyft, I would monorail to the TTC and speak with one of the transportation coordinators in the booth there near the bus area. They may be able to arrange for a driver to pick up. Or, if you really want to go over to MK, go to the outside guest relations window and tell them your situation.