In reply to Raymondo:
Yes, it seems so. I expect it's to stop touting and the likes, which would be annoying. ISTR there being quid-in-a-slot (well, CHF-in-a-slot) type Internet PCs around which you could use to book your choice on the spot.
Edit: It seems Alpybus at least have an agreement with the "Gare Routiere" (an info desk run by Geneva coach station if I recall) for them to sell tickets. This is pretty much straight in front of you as you come out of arrivals on the Swiss side of the airport (as you will if flying from anywhere but France) and isn't the Alpybus desk.
"Does AlpyBus work with Geneva Airport?
Yes, AlpyBus is an official partner of Geneva Airport. Last minute tickets can be purchased at the Gare Routière in the arrivals hall for our routes. Please note last-minute tickets purchased in the airport are more expensive than our advertised web rates."
Neil
Post edited at 09:29