In reply to cornishben:
Below is a write up from when I rode it in 2011 plus some later observations:
We did it clockwise. My feeling is that whilst anti would still be good clockwise is the best way for rideability both up and down plus you meet most of the walkers head on.
The best bit of advice I got was to look for any easier alternatives on the climbs like landy tracks. We didn’t do this on day one and ended up with a 2 hr carry up from Trelechamp.
We started at Trelechamp and carried up the Aiguillette des posettes which was about 2hrs. The descent to the col of the same name was good but short and extremely technical. Given the carry it wasn’t really worth it. We contoured round to the Col de Balme which gave an awesome and not too hard (red) descent to Trient. At the top of the col are TMB VTT signs which are best ignored.
One point worth noting is that the recommended map IGN Pays du Mont-Blanc does not show detail like buildings in Switzerland and Italy. Also Trient is not marked at all and there is no distinction between double and single track.
The section from the Col de la Forclaz to Bovine looks to have been recently re-done and is mostly rideable (up). From Bovine round to La Jure is a pig what ever direction you do it. I couldn’t see any alternative to this that didn’t involve a massive detour on the road. Definitely don't be tempted by the alternative walking route over the Fenetre d'Arpette.
La Fouly to the Grand col Ferret would be mostly rideable in the dry. We had a rotten day and the lack of traction defeated us. As the weather was so poor (snow to 2000m) we missed out the Bonatti refuge / mont de la saxe section and rode down the road instead. This is actually one of the better and more commonly ridden sections.
From Courmayeur, don't follow the walking path but the ski centre tracks, these access mostly rideable tracks above Val Veny. From below the Elizabetta hut most of the way up the Col de la Seigne is rideable.
Les Chapieux to the Col de la Croix du Bonhomme is a slog but again more rideable in the dry. The descent from here is one of the best I have ever done with only a couple of lifts over unrideable obstacles near the start. This would be a poor choice on the way up and most of the routes I saw online avoided it if going anticlockwise.
For the rest of the way to les Houches we followed the walking route to the letter and it was fine.
The Aiguille Rouge section probably has some worthwhile riding but there are bits that aren't suitable even for carrying bikes. There might be a good alternative but it would take more local knowledge than I have.
Overall thoughts? Like everything else the weather will make or break it. We had 1 nice day one cold and showery day and 2 days that just pissed it down (snow on the passes) from start to finish. This lead to a lot more carrying than might otherwise have been the case and lead us to the conclusion that it was only just worth it. Even with dry trails and good route choice you should expect some fairly long carries.
Post edited at 16:57