A correction bit is ONLY for a FINISHED horse, one that responds well to neck reining, leg aids, and the bit. If it's taking you 20 strides to slow her down from the canter, then I say you need more training, not a bigger bit. You need to go back to basics with her and teach her to yield to the bit at the walk and trot, teach her the "whoa" voice command, and get her more supple and responsive to the bridle. I would recommend having her teeth looked at by your vet as well, and have any wolf teeth pulled (yes, mares CAN get wolf teeth).
When you teach her whoa, she needs to learn that whoa means, STOP NOW, not in 2 or 20 strides. Work with her in hand first (leading from both sides), then on the lunge or round pen, then in the saddle. You should not be relying on the bit to stop her, from any gait.
I would also teach her an emergency one-rein stop, which will need to be taught in a plain snaffle (O or D ring) or a side-pull first. A one-rein stop in a shanked bit on a horse that doesn't know how well can be dangerous. However, a one-rein stop is a move that all horses should learn. It's invaluable if the horse is spooked and takes off, or one if your reins breaks or comes un-done from the bit.