Hi GI78, just to help with your planning, the trains MIGHT be back on by then, as Freeridenick says they’re due to start running again late June, but then again, they were meant to be running up to Argentiere again for this winter, so…. The bus replacement will be running if the trains aren’t, but you can’t take bikes on it. The bike bus, which you can and is very useful, only runs July & August, the same time as the bike ban.
Bikes are (or at least, last year were) allowed on the Mont Blanc tramway, LEs Houches Prarion & Bellevue gondolas , Brevent 1st stage (sometimes second stage), Flegere 1st stage, GM 1st stage, Le Tour & Vallorcine lifts. Plenty to go at…
The Tour du Mont Blanc is awesome, write up in the chamonixbikeblog linked above.
You’ll be out in the best week of the year when all (perhaps not GM right enough) the lifts will be running, there’s no bike ban (other than the year round one for the Aig Rouge national park)and the trails are nice and quiet.
Enjoy