I think driving yourself to the Hoop Dee Doo would be easier. I think you would just park in the main lot near the entrance, and from there catch an internal Fort Wilderness bus to Pioneer Hall, where the Hoop Dee Doo is held. When DH and I went to the Hoop Dee Doo in 1999, we didn't have a car. Getting there wasn't too bad - we took a bus from our resort to the MK, then took a boat from MK to Fort Wilderness. But, after Hoop Dee Doo we stayed to watch the Water Parade from the beach at Fort Wilderness, and by the time we left, MK was closed (it was off-season, so they closed early). We had to take an internal bus back to the main parking lot near the entrance to Fort Wilderness, then wait for a bus to Downtown Disney, and from there take a bus back to our resort - it took over an hour to get back to our resort.
As for getting to Cirque, take the Downtown Disney bus. There are three DD stops: DD Marketplace, PLeasure Island, and DD Westside. Get off at the Westside stop (the last of the 3) and Cirque is right there.