Bike shop switzerland
They also do group rides Thursday and Saturday although I’m not sure if they are finished by October.
From Geneva you can there is lots to go at.
On the jura side you have col du marchairuz and down to lac de joux or la barillette
Alps side. There is soo much. Col de la colombiere can be done from Geneva.
L’alpe d’heuz is about 2-3 hours drive from Geneva. Down there you also have col du galibier and col de la Croix de fer that featured on this years tour de france.
Hope the weather is OK for you. First snow on the mountains is normally the beginning of November.