Re: Where to go skiing close to Geneva by bus or train?
Geneva is indeed superconnected for winter sports, and the main hub is the airport, for obvious reasons. I mean, think about it. If you have been to any of the dozens of resorts within three hours of Geneva, you have seen people from all over the world having ski holidays there. Where do they fly in to get there? And unless they rent a car, they will need.... a shuttle.
Do a "Google" search for "Cointrin airport ski shuttles" and you will get a lot of results.
You can also go to the website of the ski resort you are interested in, and they will usually have a tab titled something like "how to get here" or "practical information." Invariably, they will have info on transport from Geneva.
As for Monts Jura (Crozet, Col de la Faucille), go to their website and under the "practical information" tab you will find a link that will take you to a Pays de Gex page where you scroll down until you find "skibus" and click to get here:
It has information on bus transportation and a shuttle (navette) from the train station