Everything is (um) up in the air right now because my flights are on NWA! It might be best, given the uncertainty, for me to make my way on arrival and arrange a meet for Wednesday. I arrive (sometime, hopefully) Tuesday evening at BWI, go downtown to hotel/dinner/crash. Speak Wednesday afternoon (the only real commitment I have the entire time). Depart BWI Thu afternoon.
Almost any hotel you choose will have a shuttle from the airport. You should not have to arrange for a taxi. We also have a light rail line connecting the airport to the city. It covers most of the high points, including the stadia.
It might be necessary to contact the hotel to connect with the shuttle, but it would be worth the slight inconvenience.
If you have not been here before, BWI is a very comfortable airport to deal with, (as airports go.)