I’m a UR student who lives in Northern Virginia.
I guess if need be, you could take the metro from one of the airports. I would assume Dulles would probably have a shuttle (or you could take a cab) to the metro (can’t tell you about Reagan, since I usually fly out of Dulles). You can get off at Alexandria, which is literally right across the street from the Alexandria Amtrak station and take the train down to Richmond/Staples Mill (this is about a 2 hour ride). You would have to take a taxi back to campus from there, which IIRC, is only like $20-30. If it is a regular break (fall, thanksgiving, winter, spring breaks), there is a free shuttle from the Staples Mill train station to campus.
There is no shuttle from airports other than the Richmond airport (those are not “local” airports, but rather airports for NoVa and DC), which is available for the above breaks for a cost of $15.
Personally, when I travel for breaks, I take the shuttle to staples mill, Amtrak to Alexandria, and my parents pick me up there (its not too far from where I live).
I think flying to Richmond would probably be a shorter commute, since you avoid having to go through switching between metro and Amtrak. Plus Amtrak always runs behind, since they dont own the tracks in VA.