done Geneva to Verbier alot of times. 8?
there is a train station in the airport, it is down in the basement. All trains go to Geneva.
The route i have done involves picking the train that goes through to Martingy and beyond, saves changing trains at Lausanne, not hard to do, just a pain carting a bike around any more than necessary. I then changed at Martingy on to the local train that goes to Le Chable, then catch a bus from Le Chable to Verbier.
The bike is in a bag. The buses from my experience are what would in the UK be refered to as coaches and as such have a luggage hold where you can dump the bike bag.
The ticket is a through ticket and covers the train and the bus. never tried but they do have a picture of a boat and i have wondered if i could get the paddle steamer from Geneva through to Montreux the tickets look the same.
The ticket office is next to left luggage above the train platforms on the same level as the airport arrivals, there are automatic dispensers but the staff speak english, or at least answer in english when i use my crap french.
Be aware that the return tickets are valid for 10 days? although i have claimed ignorance and got away with a fortnight before. i think that the return ticket price equals two single tickets anyway.
There are aload of passes but never figured out whether they would save any money.