Just found this on that web site. "Bike rentals and transportation
You can rent a bike anywhere in Denmark on a daily or weekly basis. The local tourist office will direct you to the nearest bicycle rental agency. If you would like to bike in different areas of Denmark, but do not want to go from one area to the next, there is always the train. Regional trains carry bicycles without a reservation - so you can rest your feet while the landscape rolls by. Both the cyclist and the bike must have a ticket."

Looks like badmother has been good to you.