Depending on your trip plans, you wouldn't have to ride in Luxembourg. There are extremely good train and bus systems in Europe, so you could drop the bike in a different country, and catch the train to Luxembourg.
It has been a while since I was there. I believe the main train station is in city center, with a shuttle train to the airport. Hmmm... apparently they are working on a new track to the airport. It has been a while since I was there. Still, there are buses and taxis.