It’s pretty simple to ride down to Bourg- you go down the wonderboisses trail (and then the next one, I forget the name) and it takes you down into the valley, then just carry on and eventually you’re back on the road, downhill all the way. There might well be a better way. (does it get you out of bad weather? It’s all the same valley.)
No idea how you get up to Tignes in the first place though. And you wouldn’t want to ride there for a week, though we had a lovely day there, and there’s val d’isere too. But you can also ride fairly easily to the la rosiere lift from bourg and that accesses a bunch more trails.
No expert on this as I’ve always had stevo and co to drive me around in their luxurious (smelly) van. Without transport you’re going to miss out on a lot but that doesn’t mean you couldn’t have a grand time.