AFAIK you've never been able to walk to the start line. WDW roads are generally not designed to be walkable -- designated walking paths and jogging trails aside -- and they need everyone to go through a security check. Because it is the middle of the night, they aren't going to staff every possible security point and have staff placed to guide walkers through Epcot (in the case of the Boardwalk resorts). Instead they funnel everyone through as few security points as possible. For most races that's the one main Epcot security under the monorail. For races where the monorail runs, they also staff monorail security at those resorts and a checkpoint at TTC for those who walk over from Poly to take the Epcot monorail directly.
And to answer the question about buses from Swan/Dolphin, as others have said, they run pretty much like all the other resorts. Sometimes the loop can be long if you're the last stop, so you may decide to jump off at one of the other stops and walk. The Boardwalk stop is closest if you cut across the entry and tennis courts or go through the pool and out the back.