We stayed at the Royal Plaza last month.
First, the resorts are separated into two groups, A and B. It's essentially geographically based, with the A group the three hotels on one side of Hotel Plaza Blvd (which I believe yours would be part of) and the B group the four hotels on the other.
From there, there are two theme park routes. One is Magic Kingdom/Animal Kingdom and the other is Epcot/Studios. So each route will have an A bus and a B bus. The buses start their runs on the hour and half-hour, so your hotel will be picked up a few minutes later.
Coming home is a bit trickier, as each park has a set time past the hour that the bus departs to head back to the hotel. (So :25 and :55 for example) but each route might not be the same. But this can be to your advantage, like you can hop on a B route bus, get off at the Holiday Inn and walk across the street to your hotel. (We did this in reverse when we'd *just* missed our B route bus home from the Studios and the A route bus showed up a few minutes later)
The MK bus brings you to the TTC, not the MK itself.
While the stop at Epcot on our way to the Studios wasn't too bad, our ride to Animal Kingdom was LOOONNNGGGG with having to stop at the TTC first.
There is also a lot of construction going on at the TTC. While it looks like the stops for non-Disney buses will be greatly improved when its done, its a big headache right now sometimes requiring buses to make multiple loops around the lot to get from entrance to bus stop and back around to exit.
Lastly, there is a Downtown Disney route that seems to run on a continuous circuit to all 7 Downtown Disney hotels. Not sure what time it starts, but since you're right near the Marketplace at the Wyndham it's not that big of a deal (but that's a LONG walk from the Royal Plaza in the June heat.) The bus picks up and drops off near the Pleasure Island bus stops, but not right at them. (Over where the College Program buses stop, as we learned)
-Rob
