@takios @kaia
So here you have the option of a half-fare ticket. But for longer rides, the "Velotageskarte" for 18.- is the better option. I have the all year "Velopass", which costs me around 250.- / year and, together with my GA, ensures that both my bike and I ride for free in all of Switzerland.
On some long distance trains a reservation is mandatory from ... I think May -> Sep., on other train it isn't, but i there is no room for your bike: tough luck. So far never happend to me, though.