Long ago and before my motorhoming days I spent a week (tenting) there with my family. There is at least one camp site at the foot of Alpe d'Huez. From my memory it is located on the way out of Bourg d'Oisans as you proceed to the bottom of the famous Alpe d'Huez climb.
Yes you could cycle it. My son who was 13 years old at the time hired a bicycle (typical bike hire crap! and heavy! ) and cycled it to the top. Me? I drove up in the car
Huge numbers of people cycle it every year - It is a bit of a Mecca for cyclists from all over the world.
Despite its fierce reputation it is very cyclable. Just have a reasonable bike with a couple of low gears and take your time, be patient. Slow and patient is the key.
Coming down is just as hard for different reasons.
While I was there there was a constant smell of burnt brake pad dust from cars coming down with their foot on the brakes for far too long. I saw one guy (who was on the campsite) as he came on site his back right hand wheel was in flames - basically his disc was red hot.
You could blow tyres on a bicycle too if you constantly hold the brake on while descending for that long.
Good luck
