score:4
I actually work for a chalet company who provide transport from Geneva to Morzine, there are plenty independent bus companies that will take you.
I have found previously that this http://www.morzexpress.com/ is the best option (cost effective way) to get to morzine from geneva.
Upvote:1
For anyone else with a similar question, there are several small companies that run transfers from GVA to Chamonix, Morzine and all the local ski resorts. These operate mini-buses or even coaches and the prices are in the few-tens-of-euros bracket. There are too many to list but googling "GVA Morzine Transfer" will get you an exhaustive list.
I'm not sure what the motive is for "public" transport... these are public in the sense that anyone can get on them and that you will be seated with other random people. They are also pretty cheap. They are, however, private companies run for profit (then again, so are many "public" transport companies around the world).