Wow, thanks for all the input. I have found out a bit more about the bridle she uses.
There is a guy in St. Augustine, Fl....pony boy...who is well known for his methods. If you go to his site, I think it will be obvious the kind of bridle he uses. It is something I haven't really seen before. I think I was hasty calling it a hackamore. Not really sure what it is.
The man who ownes her ascribes to this mans teaching. Very gentle and low key training.
We are going back on Saturday to spend more time with her outside the arena. I'd like to go back knowing a bit about it. I know a horse should stop in the manner it is trained. Relying on a bit to stop a horse isn't 100%.
Like I said, she goes well and stops fine in it. Being brought up with the "bit" theology, this is somewhat strange to me.....but I guess the horseless carriage was strange to some people too!
If I can, I will post a pic of her in this.