Yes, you can transport your bag in an appropriate bicycle bag provided you removed the front wheel. In this case, the bicycle is considered a carry-on bag.
If you want to take your bicycle on public transport vehicle without having it wrapped in a bag, you must buy a ticket for the bicycle, you can buy a half-fare (½) ticket for the route for it. Or, you can buy a bicycle day pass for which the cost is CHF 14 per day. So if the ½ ticket for the route is > CHF 14, buy a day pass.
You need a seat reservation during the summer half-year from 21 March through 31 October, on Fridays, Saturdays, Sundays, for all Intercity trains. In addition, for the Intercities with line number IC 2, IC 21, IC 5, and IC 51 you need a reservation on any day of the week during the mentioned period. When ever possible, try to avoid IC trains and take IR trains; they are not as fast as the IC trains yet offer more bike space and no reservation is needed.
You can read all here: Carriage of bikes on the train | SBB
I suggest you to download the SBB Mobile App. There, it is easy to buy the necessary tickets and possible reservations all in one step. Tickets are available 60 days out.
Let us know shoudl you have more queries.