At this time, I don’t believe any metro buses go to DCA, but if I’m wrong, someone please let me know & I’ll edit this post.
The 13F and 13G provide early morning service (from 5:56 to 8:01 AM on Sat and from 6:10 to 7:59 on Sun) from downtown DC to DCA on Saturday, Sunday, and holidays. Since on weekends the first Metro trains don't hit DCA until between 7:10 and 7:41, depending on what direction you're coming from, these can be essential if you're trying to catch an early morning flight.
You might also want to mention that BWI has a light rail connection to Baltimore (and the northern suburbs as far as Hunt Valley). Unlike Amtrak, I believe it actually leaves from the terminal, so you don't have an extra shuttle bus connection to worry about. On the other hand, it moves at a snail's pace