I'm going to step in and be the bad guy for a minute. :)
If you want to train better, then you need better equipment. Better-made bits are more expensive; like mylers (I think that was what the 80$ one was... or at least it looked like it. :) ) They have more weight, and a better balance, and less harsh pressure points. Tons of people (usually, not trainers) will tell you 'oh your fine with a 20$ bit! there's no difference.' They're not the ones putting the bit in THEIR mouth, are they?
If you're serious about wanting to train your horse better, then get him/her the bit she deserves. That doesn't mean, however, you have to buy brand new!
I love mylers (80-140$ range) but you check on your local craiglist listings (craiglist.org) or ebay, you can find a used one for cheaper. Mylers have all different shapes and sizes, so there's no reason you can't find one you and your horse like. HOWEVER.
Thinking like a trainer is worth it's weight in gold. Your horse is nervous, right? Instead of looking for a way to channel that nervousness (ie, a copper roller), try to figure out why
he's nervous, and fix /that/. Bits don't train horses, you do! You have to find and fix the problem, not fix the problem's quirks. He could be chewing on the bit just because he doesn't like the pressure... some horses do well with ports, or lots of pieces, or thin... you just have to figure out what your horse needs.
Here's the myler bit I use; it's very very mild, and has a low port to relieve some tongue pressure (sometimes horses foam at the mouth not because they're 'on the bit', but because they can't swallow because of the bit!) and it's broken in the center. Just giving you some ideas!
I'm a bit fanatic, so if you have any more questions, feel free. http://www.statelinetack.com/itemdy0...LT652191%20500