While flights may be cheaper on other airlines to Wash Natl or Dulles, the travel time and potential cost to those airports, bag fees and ticket change/cancel fees can quickly add up. Navigating the DC Beltway near rush hours for Dulles trip requires lots of additional time and a dash of nail-biting.
As sponsors, we run mids back and forth to BWI all the time. We live 17 miles from the airport, and on mass-movement days, have made 2-3 RTs in one day. We agreed one time to help a plebe get to the airport, and the (bless his heart) plebe told us his flight was out of Dulles when my husband picked him up - at 3:30 pm, for a 5:45 pm flight. Anyone who lives around here knows that's a road race situation. My DH and FFP (former fighter pilot) got the plebe there in time, and returned home, 6 hours later, fighting his way through rush hour both ways. "Don't ask," he said. We don't offer Dulles rides, but suggest a shared shuttle ($$$). If convenient, we will run them to New Carrollton Metro Station about 20 miles from Annapolis, and they can Metro right to the Wash Natl Metro stop.
At BWI, during common travel days, there are always mids, sponsors, families willing to help out with rides.
As has been recommended here many times, teach your mid the ropes, then let them book their own travel, a valuable life skill.