Most definitely check with the front desk, though most off-site resorts would only run one or two vans (if they have them). Most of their shuttle work is contracted out so they usually do not operate a hotel shuttle any longer.
I think whats missed here is that the Regal Sun, Hilton and Buena Vista Palace are just across the street from Saratoga. The Best Western is the greatest distance away along Hotel Plaza and it is just at a mile.
Also to clarify my thoughts
taxi to the start and walk over to the bus area after you finish and take the bus back to the hotel you are staying at. Their stop is off to the far right as you look at the Epcot entrance (past the monorail station). Though there are a few taxis standing at the finish area usually.