It’s a great area for biking especially out of the main summer tourist season – with the added benefit of super food! I’ve done quite a bit of biking there, although mostly 3/4 day trips on the road bike. I did a lovely 2 day mtb trip on Seiseralm – I can tell you more details if you want. Will you have a car (the trains are pretty good, you just need to be more organised)? And overnight trips here are really easy because to stay in a mountain hut you just need a hut sleeping bag (a liner really) and you can pick up all your food and drink at a reasonable price there.
Otherwise the links I know are just in German:
South Tirol routes
Mountainbike Dolomiten (although it’s a book)