Buses start running, every morning, from resorts to the parks, by 6:30. They don't run as frequently as the 'regular' buses do.....up to about an hour prior to opening. If you just miss one, it could be almost 30 mins before another comes, or, it could be just 10. No way to be sure.
As far as the regular buses go, they are supposed to arrive every 20 mins. If you get to the bus stop just as your desired bus is leaving, it could be 20 or so mins before another one comes along. But it could be less. There are overheard arrival boards that will give you the anticipated arrival times of the buses. But, they can, and do, change, depending on traffic.