The DME buses are like charter buses, with the plush seats and tvs. There is a chance they have a bathroom on board, but I can't remember. The trips from MCO to the resorts are generally not more than an hour though, including all stops.
The on-site transportation from resort to park and park to park are standard city buses run by Disney. So, no bathroom. These trips typically are no longer than 45 minutes including traffic and other stops.
Disney World: 10/92 Yacht Club, 11/96 Disney Institute, 12/00 Yacht Club, 6/05 Beach Club, 8/06 Shades of Green, 8/07 Caribbean Beach Resort, 10/07 Coronado Springs, 12/08 French Quarter, 3/10 All Star Sports, 4/12 Port Orleans Riverside
Disneyland: 1987, 1997, 2002, 2008, 2010, 2013