I concur with the stay at Dulles the first night, then its a matter of what your time is worth. There is a MetroBus that goes about once an hour from IAD to Roslyn Metro, then transfer to the metro blue line and get off at DCA. That is likely the best public transport option that is available.
The cost of the 5A bus went up, and so are metro fares so i don't know the actual cost. Check the wmata.com site for fare and schedule