Riders, bits, and horses... so many options. I wonder what bit she was ridden in before? Way back when I lived and breathed horses I had dozens of bits. Different horses, different levels of training...
I can tell you what I don't like. I don't like a broken bit with a long shank and a curb chain. It literally puts the horses jaw into a vise causing all kinds of problems. I had a barrel racing mare that I rode with that type of bit ONLY when we were racing and only because in the arena she had no whoa, lol. We went out of town and a neighbor decided to ride my horse, without permission, while we were gone. He used my racing bridle. When I got home my horse's tongue had almost been cut off. I have never been so furious in my life.
Also, broken bits (snaffle type) can put a lot of pressure on the bars of the horses mouth - depending on the rider of course. (not saying this rider is doing that!) If the horse has bad teeth that bit may very easily be bumping the teeth every time she's being direct reined. I strongly suggest teaching the horse to neck rein.
I just saw that
@SageHill mentioned rubber bits. I think that's definitely worth a try - especially if it's curved to give the horse's tongue some room.
I think it will be trial and error with this mare. She may be spoiled like Mini suggested or stubborn, or she may be reacting to pain. In my experience a horse that is dead set on bucking, just to buck, will put their head down, round their back, and cut loose. A horse that's reacting to pain, or trying to evade pressure, will toss that head back with an open mouth and a hollow back.
Just my 2cents...