There are numerous cycle paths that run between the airport and Geneva. Best of all, most are dedicated paths meaning you won't have to share space with cars or busses. The one big exception is once you arrive at the airport, where cycle path runs out and you must share the road with busses and cars.
Once at the airport there is bike parking but spaces can fill up fairly fast so get there early.
The official airport web site has a downloadable cycle path map. But it is not all that easy to read when printed so you might want to try and find a better map at a tourist information office.