Can't tell you about the local area - but I'd suggest finding a removal company or freight forwarder - I bought a whole load of packing materials (including bubble wrap) from a freight company a while ago.
Since this is a request for help, I'm moving this message from General to Help and Tips.
I saw large rolls (1m long by 40cm in diameter) at the Migros, or Coop or Post Office in Neuchatel, cannot remember which but this town is also French speaking so maybe that helps for Geneva too I am not sure.
If you need more bubble wrap, or want free stuff, maybe ask at a computer shop or furniture store. Oh, and bring a wife/girlfriend if you are not female, it works much better if she asks.