I decided to move ahead to the next level of the S-train experience for my trip down to Valby this evening: taking my bicycle on the train. It turned out to be very simple: I bought one ticket for me (20 DKK), and another ticket for my bicycle (12 DKK):

When the train arrived on the platform, the first carriage had a huge image of a bicycle painted on its side, so it wasn’t hard to figure out which carriage was meant for me.