I have gone to DC via BWI many times using SWA. It’s pretty easy with the Mark & Metro.
In this case my brother, who can’t come, gave me airline points for a free ticket into Reagan National. I’ll take the Metro from there to the Sheraton. I should be able to avoid cabs entirely.
Your info is good, though, and someone else will benefit from it.
Transportation info from the Sheraton’s site:
“Shuttle Service: If you are flying into Ronald Reagan National Airport, we provide complimentary shuttle service every 30 minutes from 6 AM until 11 PM. Simply call the hotel from the courtesy phones available at each terminal for shuttle pickup.”
Probably a good idea to confirm this though.