Looks like it may be pretty close on price, either SK CPH-IAD/UA IAD-RDU or BA CPH-LGW/AA LGW-RDU. Check it several ways to see what will produce the best price. You may want to look at what will do you the most good on miles/points for your favorite alliance.
Bus or train is not really an option - we have nothing like the European intercity networks, except for some convenient train coverage in the northeast. Stick with the flights.
And yes, you did get the plural spelling on "bus" correct - "busses" is actually the plural of "buss," an old term for kiss. I always laugh when I see a sign at a bus station directing people to "busses" - I want to ask just who's doing the kissing! (Welcome to irregular plural forms.)
Enjoy your trip, and if you have some time, try to stop in Washington if you've never visited our capital - there's plenty to do, and you can hit some of the high points even in a day or so.
[This message has been edited by fcrit (edited Jan 04, 2004).]