Not aware of any buses that go to Fantasia Gardens.
I would take a bus to Swan/Dolphin or Boardwalk. Its not a long walk from there. Swan/Dolphin will be closer .
An alternative to taking the bus to Swan/Dolphin is walking from Hollywood Studios to Fantasia Gardens. It's a ~20 minute walk that will take you past the back of the Boardwalk Inn.
Not aware of any buses that go to Fantasia Gardens.
I would take a bus to Swan/Dolphin or Boardwalk. Its not a long walk from there. Swan/Dolphin will be closer .
If you click BW Villas on this page, it says buses are operating between BW and Disney theme parks, so I would assume that includes DHS. They also suggest the Skyliner to DHS, but DHS is not explicitly excluded in the bus info.
Certainly not a definitive yes, though.
Swan/Dolphin, which is where you would best want to go for FG, is not a Disney resort so it's not on that page, and I can't find any updates on their own web site.