American Airlines has flights from Dallas (DFW) to Washington D.C. or Baltimore (BWI) for $103, NONSTOP. $52 each-way. Flights February to mid-April. A few Saturday departures available in February, other months are Tuesday/Wednesday only.
Note: Carry-on bag is allowed for free. You can avoid seat selection fees if you accept a randomly assigned seat at the gate.
Note: Spirit has price matched flights with inferior, fee encumbered fares that charge a $30 to $35 dollar fee for to bring a bag. Spirit flights should probably be avoided unless you can fit everything you need in a small “personal-item” like a laptop-bag, or Jansport Backpack.