But now for some tips on how to take your bike on a train. First in Germany.
Traveling with the Deutsche Bahn in Germany
First of all. If you travel more than once, I would get a Probe BahnCard. For the trial I would likely get the 50% one. For more permanent use, I always get the 25% one.
BahnCard50 is great when you want to be flexible. You'll always get 50% discount. Which is great when you quickly need to book a trip. This might be especially the case when you're traveling with your bike.
BahnCard25 is great when you can plan a bit in advance. By default you'll get 25% discount, but you can get a lot more too. Just recently I got a ticket that is usually 100 Euros for 12.90 Euros. But I booked it two weeks in advance.
German trains are very expensive without any discounts, so it's pretty much worthwhile to get a Probe BahnCard when traveling in Germany. You can use it immediately and it's valid for three months, you just need to make sure that you cancel it in time.
Prices, rules and regulations can be found here: https://www.bahn.com/en/offers/bahncard