There are several ways to get from Washington's Airports to OC. Here are a few I recommend:
If you are at Dulles Airport:
For a more flexible, but more expensive option, take the shuttle van from Dulles to BWI airport (about $90) you can take the Bay Runner shuttle to Ocean City. It is about $100 and runs frequently.
More information on Dulles to BWI shuttles can be found at
http://www.theairportshuttle.com/
More information on Bay Runner Shuttles can be found here
http://www.bayrunners.com/
For a less expensive option but less flexible option, take a taxi from Dulles to the East Falls Church Metro station. From there you can take the Metro Orange Line to the east end at New Carrollton, MD. You can then take a Greyhound Bus from New Carrollton Metro Station to Ocean City (call 800.231.2222 or go to
https://www.greyhound.com/farefinder/step1.aspx to reserve tickets). There is one bus a day which leaves New Carrollton at 11:35AM and arrives in OC at 3PM. You don't need to change buses, and the 3.5 hour time is not bad for a bus trip to OC. Cost is between $30 and $60 dollars depending when you buy your ticket and other options you select.
If you are at National Airport:
For a more flexible option, but also more expensive and complex, take the Metro from the airport to New Carrollton Metro Station (Metro Yellow Line to Orange Line)and then take the MARC train (the stations are co-located) to BWI Airport. From BWI take the Bay Runner Shuttle to OC (see above for more info on the Bay Runner shuttle).
For a less expensive option that is less complex, but less flexible, take the Metro from the airport to New Carrollton and then take the bus to OC. See above for more info on the bus.