In reply to Jock:
Hi Jock, I live in Chamonix and have ridden the TdMB...
The snow level is rising, but it's still sitting at just a bit over 2000m and some of the accumulations are going to take a long time to shift. I'd consider heading further south, Finale/Provence sort of way, if you want to link up stuff with big days and not worry about the snow, it's just not really possible here right now.
Saying that, the lifts open in CHX at the weekend so you could just stay in a hostel and have a weeks riding here from the lifts and through in Courmayeur under your own steam. Versant Sud do a very good MTB guide to the Aosta Valley which you can pick up locally. The Chamonix Bike Book is now in it's second edition and has lots of good rides for the CHX valley. And if you want more inspiration, I've got a bike blog, complete with a write up of the TdMB...
http://chamonixbikeblog.wordpress.com/2012/08/16/tour-du-mont-blanc-day-1/