What sort of bit is it that she dislikes?
Mia chews on a bit without a roller when she is nervous or when she wants relief for her tongue or when she is bored...a bit general, I know, but that is the best guess I have based on lots of bits and watching her.
She is less likely to chew on a bit with a port, such as:
If she has a bit with a roller, she'll play with the roller:
An odd choice is a Billy Allen. It is straight across with minimal tongue relief, but I think it has a broad, even pressure that doesn't make her seek relief. They also have rollers in the middle, although she doesn't play with that style of roller as much as a fat copper one.
Mia rarely tosses her head, but I've read that it can be a sign of seeking tongue relief. And in all honesty, she is more likely to chew on the bit and toss her head if I am heavy handed. It could be a symptom of how the current owner rides more than a preference of the horse.