Hey and welcome!

With the local trains you need a bicycle ticket, but NO RESERVATION. So just buy your tickets for your self (maybee you find a cheap offer online) and when you reach the train station, buy a ticket for your bikes on the local vending machines. It will cost you around up to 6€ per bike.

It gets complicated when you want to take you bikes with you in the faster trains like IC (InterCity) & ICE (InterCityExpress) here you NEED a RESERVATION on top of your bike Ticket (9€). But you can only buy this reservation only at a ticket counter (and maybe from the hotline as well).
You even can't get the information if the bike spaces are already booked out online. sorry!


I hope this helped.