I have never had a problem getting to the parks either in the morning or in the afternoon. The busses usually run every 15-20 minutes or so. There are busses for each park, water park, and DD. It also may depend on which bus stop you are at. For example, if you go to WDW during a busy season and you are at one of the last pick ups there may be a lot of people on the bus. Just prepare accordingly. By this I mean, make sure you leave a bit early for the parks. Keep in mind security check once you get there as well!
You may consider posting on the transporation board too.
Melissa