Sabrina,
Thanks for writing! Getting to some Fort Wilderness Resort (FWR) activities (
Hoop-Dee-Doo, Campfire Sing-Along, etc.) can take time, since the Disney bus drops you off on the south side of FWR, and most activities require you to take a separate internal FWR bus to get to your final destination. In the case of Hoop-Dee-Doo, you'll need to get to Pioneer Hall which is on the North side (near Bay Lake).
The options that I can think of are:
1. Disney's Hollywood Studios (DHS) to Magic Kingdom (MK) by bus, then take boat to FWR, which arrives on the north side, near Pioneer Hall
2. DHS to FWR by bus, and then take the internal FWR bus to Pioneer Hall
3. DHS to Disney's Wilderness Lodge (WL) by bus, walk to the WL boat dock, then take the boat to FW
4. DHS to WL by bus, and then walk to Pioneer Hall (it's a little over a 1/2 mile, but can be a nice walk)
Of these options, I think the first one is the most pleasant journey, as it takes you by the MK and gives you a nice boat ride.
Since waiting time is the biggest unknown in the timing of any of these options (and COULD make any option the fastest or slowest), if I wanted the fastest route I would wait to see which bus comes first at DHS and then take that route (e.g., if a WL bus comes first, I would go with option 3 or 4). This way you help shorten your first wait.
I don't think a rental car will save you much time, but if I had a car, I'd drive to FWR and take the internal FWR bus to Pioneer Hall.
By the way, I would definitely reserve at least an hour (probably a bit more) for the trip. If you get there early, there is plenty to keep you entertained (kiosk shop, photographer, look around Pioneer Hall, etc.)