I think the busses start running an hour before the parks open. Swan is the first stop, so you shouldn't have any problem getting on. You won't be able to get into Epcot before the park opens to catch the monorail, but I love the idea if you're heading out after 9 a.m., or on an EE day. If you're going at a busy time of year, you may want to ask someone at the hotel if traffic will be bad. It seems like the busses we were on passed a lot of cars stuck in traffic to get into the parks.
We had a 8 a.m. PS at AK on a non-EE day (enough abbrev. for ya??LOL) Anyway, the bus came at 8 a.m. We were told they hold the PS for 15 minutes, but we were probably there a little later, and it was no problem, just bring you PS conf. # or printout.
BTW, at the Dolphin the concierage desk did a really good job finding PS's for us for the next day. I'm sure the Swan would be just as good, and we were there right before July 4th.
It's really nice having a PS before the park opens. We avoided the EE parks, as we heard they were actually more crowded.