The Dr. Bristol bit is no longer allowed in dreddage competitions. The second bit should be okay. The USEF is the governing body that sets the dressage competition rules. The portion on bits is D120 (pgs. D26-D28). http://www.usef.org/documents/ruleBook/2012/08-DR.pdf
If correctly taught, dressage will reform a hard mouthed horse to move lightly and obediently from a snaffle. You should call your dressage instructor prior to your lesson and ask her what tack you will need, and if what you have is acceptable for the lesson.
Dressage doesn't take brute strength, but it requires a really strong core (abdomin/lower back area) for balance and absorbing the movement of the horse. It's more important to be flexible and toned. I've hear many dressage riders swear that Pilates was excellent for increasing the strength and flexibility they needed to be better riders. I've had good success with Tai Chi and Yoga. Running helps build your aerobic capabilities (needed for dressage).
I'm so happy you're interested in dressage! I hope you enjoy it as much as I do. And remember, it's really important to find an instructor who is knowledgable and can break the concepts down into easily understood parts. If you don't understand something, ask.
One of the problems with dressage is that it's extremely difficult to learn on your own. What I would start with is working on your position. You should also start thinking about where your weight is in the saddle (is the weight evenly on both seat bones, just one?). I would spend the time learning as much as possible about the rider aids and how those influence the horse. I would stay away from attempting to train the horse specifically for dressage. It's more important that you can use your body to help the horse, or get out of his way so he can do what he needs to do.
Good luck! I hope you love it. :) Posted via Mobile Device