Bullet proof vests don't use just a handful of layers. I don't know how much your supplies would cost but 30+ layers of kevlar plus epoxy around a bell means material costs beyond $100 for me. So I think the trans blanket suggestion was a good one, unless you really want to get the experience.

If you worked for an exotic car mfr (front engine/trans) and they wanted something more classy than a blanket I think this is a really good idea. You could even take it to the firing range and put a small caliber bullet through it as a simulation. I wouldn't bother with the carbon fiber.