Where are you coming from and where in DC are you staying?

If I was on a short non-stop coming in and was staying reasonably close to union station, I'd do BWI & Amtrak. Shuttle bus takes you from the airport to the station, and it's about 40 minutes (I think!) to Union Station in DC. You should be able to figure your trip times and costs on Amtrak's website.

I would not do the bus via Greenbelt--a change, and a long time on transit make it completely unappealing.