We stayed at Stovall's last October and found the walk to be not a big deal but I totally understand wanting to save your feet a bit! According to the ART website, there are ART stops in front of BW Pavilions, BW Stovall's, and the Annabella hotel for Bus route #9.
Also according to their website, you cannot buy ART passes on board the bus. If you don't have a pass ahead of time, you have to pay exact fare and they can't give you change, so make sure you have the right amount of cash available.