Hi srtraveler. I live near Burlington and have cycled all the roads on the Green Mountains Loop, most of them many times. Mosquitoes are present but rarely a problem during the day in July and August, but you will want netting on the tent.
Accommodations (both with and without walls) are plentiful and range widely in price. I would start with the Cyclists Yellow Pages Online at Adventure Cycling. Follow the link for the Vermont state agencies to the public campgrounds for rates. The popular ones fill up, so plan on reservations. Prices for private campgrounds and motels are easy to find on the web, of course.
I'd like to suggest that you pamper yourselves with one night at a good country inn, especially if you have never had that experience. It will cost perhaps 1.5 times the motel price, but it's hard to beat relaxing by the fireplace with a glass of sherry in hand before dinner. Awaking in the canopied four-poster and going down to a huge breakfast isn't bad either! Plan a late start to the riding that day.