As a first timer to WDW and obviously to the Swan, waiting until after 6PM to check in was completely unacceptable when our check-in time was 3PM. My children should have been in their bed not sleeping in the lobby. That truly colored my experience with this hotel and I let them at the hotel and their CS online know of our experience.
There is common confusion around this.
There is no such thing as '3pm check-in time' at any of the Disney resorts. That is just the earliest possible time your room could be available. At non-busy times, the rooms can be available much earlier than that.
During peak times.. the room may not be available till 6pm.
You were travelling during a time period when all the resorts on property, including the Swan & Dolphin were nearly completely full ... or "boxed" as they refer to it.
This means that everything can take longer than usual : check-in, transportation.. everything. Mostly because everything is running at 100% capacity or worse.
As for the transportation, 20 minutes would have been tolerable but I can say we definitely waited longer than that in the morning, early evening and later in the night. We did appreciate the service but it could have been more...
It's very likely you could have had that same experience at a Disney resort during the week you travelled for the same exact reasons. Everything was at capacity which means even the slightest little hitch can really slow everything down.
I might be mistaken, but I believe that Swan/Dophin transportation is handled by the same people who do all the other resorts, so if it was slow there, odds are it was slow everywhere that week. [EDIT: Nope, I was wrong on this.. it IS separate transportation]
Early morning and evening are the busiest times for transportation and I know there are a few times that I've waited 45 minutes or longer for a bus to a Disney resort leaving a theme park during a non-peak travel period so it doesn't surprise me you had that experience when all resorts were near 100% capacity.
Sorry your trip was less than magical, but travelling during peak time periods comes with its own set of concerns that you do kinda have to be prepared for and plan around.
From mid-June to early August is very much a peak time period for travel to Disney.
Knox