I've only seen that bit in person once, advertised--aptly--as a "Whoa Horse." I wondered if you were talking about it, but the picture of the Walker bit threw me off. That bit is NOT meant to be ridden on contact. It should only be used by very experienced riders, and then with a draped rein. The point of the curb is to intimidate the horse into having a quick stop. You slam them into the ground a couple times, and they won't soon forget that pain. From then on, every time you touch the reins they sit down and slam on the brakes.
Do not, I repeat, do not use it anymore, or you run the risk not only of causing your horse pain, but of permanently ruining her mouth (or causing her to rear from the pressure--that curb can even break a jaw). It's also time to stop taking advice from Mr. Neighbor....not all "experts" are as they claim to be.
Instead, if you are somehow able to find competent instruction, and a trainer who is willing to work with both your horse and you, that is the avenue I would take. No bit can prevent a horse from running away, but a good rider can prevent a dangerous bolting episode on any horse with any bit. But you have to know how to use the tools appropriately for your horse (and how to choose the correct one).