Just FWIW, here is the curb bit I'm using with Mia:
Some of the things I like about it:
No joint in the middle that folds.
Each side can be pulled back 45 deg before the other side starts to move.
Each side can swivel out to the side on its own.
Not very thick or very thin - kind of a "Momma Bear" thickness.
Because of the 45 deg of pull allowed, I can pull back on one rein and it looks like all that does is put some pressure on the bar on that side. That normally is a pinkie of pressure on the rein, but it seems to work when Mia tries to tip her nose to the outside of the turn.
Another that I tried with her looks like this:
It worked OK, and at $13 is dirt cheap. Mia liked playing with the copper rings, but she didn't seem to neck rein as well with it. I'm going to try it with Trooper just to see how he does in it. Mia will probably stay in the top bit for some time because she seems to "understand" it well. It isn't a solution to her problems by itself...the work we do practicing stops and neck reining is a critical part of what she needed as well. Used WITH training instead of as a substitute for training, changing bits can help.