Well, in the Netherlands and at least some other EU countries most train stations have a bike rental system that works by just using a card to unlock the bike for a couple of Euros for 24 hours. So there is a possible solution.
Many people here use that system. It’s also possible to buy a (second-hand) bike and park it at the station where you need it, if you’d like.
Edit: Didn’t see the post below… but exactly that.