can i bring my bike to the train or bus to this place?
In the local train indeed yes.
Yes you can bring your bike to either to the train or to the bus. As majority of the population in Denmark uses bicycle, they even have alloted some spaces like in the train for those who are using bikes.
Denmark is quite friendly towards people bringing their bikes on public transports, so I’m guessing it is possible. The question is more related to public transports questions than Frediksborg. Check with DSB (danish public transport) to find out prices and other information.
Get quick answers from Frederiksborg Castle staff and past visitors.