Lufthansa charges $200 each way, they have a non-stop from Denver to Frankfurt.
British Airways allows one checked bag on flights to Europe, your bicycle counts as your second bag and costs 32 pounds. It appears that if you could check your bicycle and carry everything else in a carry-on bag, there wouldn't be a charge.
I took my bicycle on British Airways for free last May, and I took my bicycle for free on Lufthansa in May 2006. traveling with a bicycle isn't what it used to be.
If you go with British Airways, be aware that the flight from Denver lands at Heathrow, and most of the onward flights to the continent leave from Gatwick, about 30 miles away. When I flew to Sicily in 2008, I cycled from Heathrow to Gatwick, but it wasn't easy.