I just hiked the LT southbound in July, so here's my experience:
1. For the entire length of the LT, I never used my tent, except the night after I finished in MA. Shelters are plentiful, with the farthest distance being about 8 miles apart. In one place, there are 3 shelters within 6 miles. In October, they will also not be crowded by groups, which was the reason I carried a tent with me (and almost needed it twice).
My point is, you actually don't need a shelter at all--although you might want to carry one for security and flexibility (I liked having the option of camping anywhere, although I didn't ever do so).
2. Bugs will almost certainly not be an issue. They never bothered me in July, so why would they be around in October?
3. Unless you're very careful about where you camp, there'll be some cold nights. I'm talking not only 15 degrees, but also windchill because there are a ton of shelters at high (for VT) elevations. The shelters on Mansfield (Taft and Butler) are 4 walled, but the ridgeline to the North (Sterling Pond and Whiteface) is very exposed and the shelters are 3 walled. The secret here is that the 4 walled ski hut is unlocked, and very warm. I slept in the hut and was much warmer than those who slept in the Sterling Pond shelter, who set up their tents inside the shelter to endure sub-40 degree temperatures chilled further by high winds (this was in the midst of the hottest July on record).
4. Having grown up on the VT/NH border, I will also tell you that we have often had snow days (school closed) before Halloween. Never more than 2-3 inches, but it's something to be prepared for.
I would seriously recommend a lower rated sleeping bag or a liner. When you're out there for that length of time, the warmth is well worth the weight.
If you have any more questions about the trail or general October VT weather, I'm a resource.