In reply to Graham Stephenson: Although it will feel a bit uncertain, your best (and cheapest) bet is likely to be to ask around with the Tour Ops when in resort. You're coming and going from major resorts on a Saturday judging by your dates so there will be dozens of transfer coaches on all the major routes + there's only one of you. Although transfer reps are not meant to accept cash in hand for hitch-hikers many do since it's a nice little side-earner for them.
If you can find someone willing to take you from VT to Geneva airport then you can either get one of the many shuttle services to Chamonix or try and blag your way on to another transfer coach. Same thing coming back and even if you can't find a transfer coach from Geneva to La Plagne, you'll find one Geneva to BSM and can get a bus / taxi from there to LP.