Let me elaborate a little more. For most trains in Switzeland, you don't need a reservation for a bike. However, for the ICN (white, tilting) trains you do. This costs an additional 5 CHF, and must be made at least 30 minutes prior to departure (but sometimes they will let you get away with doing less). You can either go to the ticket counter or phone the SBB to make the reservation, but if you do it by phone then you still need to pay for it and pick it up at the ticket counter - yes, this is very annoying!
The best solution is to avoid these trains whenever possible. To get from Zurich to Nyon, you could have taken an IC train direct to Lausanne (which travels on the line via Bern) and then taken any train to Nyon, and you then would not have needed a reservation for the bike, just the regular bike ticket. Furthermore, these ICN trains between Geneva or Lausanne and Basel or Zurich/St Gallen alternate their origin and destination every hour. They make the switching between train simple by having the two trains line-up side-by-side in Biel / Bienne, but if you need to change from one ICN to another then you need to pay the 5 CHF reservation fee twice - this is even more annoying. On the SBB website, when you search for different train time options, there will be symbols next to the train if a bike reservation is needed. As mentioned above, during the colder months, no reservations are needed on the ICN trains.
Another way to avoid this hassle is to use a bike bag. You can get one for about 80 CHF, they fold up pretty small and only weigh about 1 kg. You then don't need a ticket for the bike or a reservation, but you can still store the bike in the normal bike compartments of the train (although if someone comes along with a bike which they have paid for then you must make room for them). See the thread
Taking a bike on the train for free.
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