The short answer is yes. On all Danish train routes, you can bring an ordinary bicycle (unfortunately not cargo and tandem bikes). Bike trailers must be folded together and brought as hand luggage.
At DSB, a ticket for your bike costs DKK 20, regardless of how far you travel. It can be purchased via dsb.dk or the DSB app immediately before departure. Please note that the space for bikes on Intercity and IntercityLyn trains are limited. Those are the train types that cross the Great Belt, and as a train ride is the only possibility here, you may want to book you ticket in good time.
In the local S-trains in the capital area, bicycles are free of charge, and you can bring cargo bikes and tandems as well. More and more bus companies also allow bicycles to be taken along. But the available space is limited, and it is only on some regional busses you can book a place in advance. Check the options at the relevant company if you plan to bring your bike on the bus.