I've not seen a direct (no stops) route. It doesn't mean that there isn't one, just saying I've not seen one. You will not have to transfer, but beware you might make stops to load and unload. From what I've seen, the route is:
1. Disney’s Boardwalk Inn
2. Disney’s Yacht Club Resort
3. Disney’s Beach Club Resort
4. Walt Disney World Swan / Dolphin Resort
Reverse the order for the ride back to Epcot from HS.
I have no idea how long this takes, that's something I have to search for soon, but websites I see so far say it might take longer than walking. I plan to use these a few times when returning to swan and hopping between epcot and hs myself, but for rope drop, we're walking. Principal Tinker has a great point about the Boardwalk. I've never been yet, but it might be worth checking out for you between HS and EP. I'm definitely stopping because I read about some bakery treat that is a must do. Can't think of the name right now. I'll research the time estimates, and post back here.