Might be worth bumping this a bit later in the year as there may be some alpe d’Huez residents with cars.
The most exotic way would be to helicopter over to les Deux Alpes and ski over from there but it may not be practical with timings.
Otherwise there is a VFD bus service from l’Alpe d’Huez down to Bourg d’Oisans then it is 35 minutes on the bus from Bourg to la Grave. The timetables are not out yet, vfd’s website is http://www.vfd.fr (for trainspotter points: vfd used to run a train service to Bourg before the rail line was ripped up, the bus station was the old train terminus).