As noted, the buses to the parks start by 6:30...but they tend to run less frequently than the 'regular' buses do. So, if you miss the 6:30 bus (or thereabouts), you may have to wait up to 25 mins. Now, having said that, I have arrived at the bus stop as 'my' bus was departing. But, I usually didn't have to wait more than 10/15 mins for the next one. I'm not sure if the departing bus calls it in that there are people waiting or what....maybe.
The only time you have to worry is if you have, for instance, an early breakfast ADR, at a nearby resort. If you have to be at, say, 1900 Park Fare, at the GF, for 7:45am, you need to be out at the MK bus stop by 6:45. That way, if you just miss the bus, you will be on the next one. Then, you will take time getting the monorail over to the GF from MK, or perhaps the boats will be running. But, you do need to plan accordingly and leave plenty of time for early morning travel.
