You may be fined if you don't. If you do not want to take of your own bicycle, you may send it ahead as registered luggage. Instead try to travel on one of the few trains between Hamburg and Jutland which have an open spaced postal wagen. These busses ar often run by the Danish Railroads. Almost all county busses have room for two bicycles in the rear luggage room.
Prams have priority over bicycles.
You may have to load the bicycle yourself, but ask for help if you do not know how it works. Remember to take all luggage off before stopping the bus. There are a growing number of long distance coaches in Denmark. These are less well known, which is a shame. They are often run to and from areas or on routes where the train service is poor.