I have biked in Europe many times, including Denmark. I have never shipped my bike ahead of time, so I can't help you there. I have always taken the bike with me on the plane.
Most (but not all) airlines will let you take your bike on an international flight for free, counting as one piece of luggage. You can either get a box from your local bicycle shop and pack the bike (probably the safest). Either the bike shop can pakc it for you and you can do it yourself. In addition, most airlines will let you buy a generic box, for $15 or more, to put your bike in. For airline boxes, all you need to do is loosen and turn your handlebars (you may have to disconnect brake cable if not long enough) and take the pedals off. You can usually get a box from at the airport, but then you have to stand in line twice: once to get the box, and then to check-in. So allow enough time. You can also put other things in the box to cushion the bike, like bikepads, or sleeping bags.
When you return, you can arrange to get a box from a bicycle store near the airport, not an easy thing to do. Or you get a box from the airlines. Some of the airlines only give you a big plastic bag to put your bike in. I'm always scared when that happens, but nothing serious has happened yet.
Double-double check with the airline about their policy on taking bikes. Usually they don't know!! I have gotten different answers, so it's worthwhile to do the homework ahead of time.
When you get to the airport in Denmark (Kalstrup?), just a nice out-of-the-way place to spread out and assemble your bike. I have put my bike together in some of the finest airports in Europe: Hamburg, Gatwick, DeGaulle, Frankfurt, Shannon.
Wish you luck.
I have never taken a BOB, so I can't help you there.