The busses to each theme park theoretically begin running one hour prior to that park's opening. So unless yu are eating at Chef Mickeys on a MK early entry day, you'll need to take a cab. You could try taking the very first bus to the AK, then taking the bus from there to BC or Chef Mickeys, but I wouldn't count on the connections being good enough to make it.
BTW- It costs about $20 to get to the Contemporary from the AS, and probably about $14 to the BC, plus tips. When you start adding that to the cost of your airport transfers, you might be better off just renting a car for the week.
Anne