Originally Posted by violist

I'm guessing that if you're going to be in the Capitol building, you
won't have an enormous amount of luggage. You can walk to
Union Station easily in 15 minutes, and public trans will take
longer than that. If you are going to cut things close, a taxi
to Union Station might be sensible.

There are trains at 3:34 (arriving BWI at 4:12) and 4:20
(arriving 4:45). I'd say the latter would give you enough
time, even though there is no elite security at Pier D.