See Mears Transportation Shuttle Services at
http://www.mearstransportation.com/ShuttleServices.htm
If you use Mears Transportation to go to the Swan/Dolphin, there's no guarantee you'll actually be on a DME motorcoach. Disney provides DME motorcoach transportation to those
Disney Cruise Line guests who have land accommodations at the Swan/Dolphin as part of a land and sea package. Those guests check in at the DME "Disney Welcome Center" and they travel with other DME guests. Disney contracts with Mears to operate the DME motorcoaches.
However, passengers who use the regular Mears Shuttle service, which picks up on the "A" side and the "B" side of the airport, are likely to be on a Mears shuttle, and might stop at off-site hotels before continuing to the Swan/Dolphin. So don't count on a DME motorcoach.