What it sounds like to me is a misunderstanding between Equitation and Horsemanship. You have a real need for learning of Horsemanship. Might I suggest you read this? Horsemanship and Equitation
As far as bits go, IF she rides well in it and you can control her with it, why change it to suite some one else?
When I was much greener (and convinced that I had all this stuff figured out) a poor horseman shared with me a nugget of wisdom that I'll share with you. I was explaining to him what so and so famous horseman had said he said to me, "That guy is a master and he has 10 answers for every question. You have one answer for 10 questions."
People who are very competent with horses and teaching others about them DON'T get all wrapped up in all of the small details because they see LOTS of paths to that destination. People who freak out over minutiae have one path and it frequently is littered with potholes... Good luck!