Bicycling, I tend to be more of urban/costal tourer, but motorcycling I like rural touring and have been looking into VT dual-sport (on-off road) routes.... probably similar roads that would be good with gravel/adventure bikes.
THIS thread has long distance dual-sport trails through VT (AT, TET, NEAT, PD). But if you're only looking for a night or two camping, then I'd look at VT's town highway maps and look for class 3&4 (gravel and unimproved) roads
HERE.
As far as camping is concerned VT permits dispersed camping in much of its National Forests, State Forests, and Wildlife Management Areas - just google it and follow their reasonable rules. Personally with a bicycle, I'd just follow any gravel road into a national or state forest, bushwhack till your out of the road's sight (but further if you want a camp fire) and camp. Fill up an extra 2Ls water at some stream along the way for navy shower at camp.