An idea is to leave the headstall and bit on the horse when she is stalled. Let her wear this for a hour or two, see how much she is still chewing at the end of your time limit. I would do this several days in a row, before or after her work session. Then I would give horse a little bit of hay to chew on. We used smooth ring sided snaffles, about 3/8" thick. Thicker mouthpieces may be too big for a young horse to deal with yet, can’t close his jaw and lips. Thinner mouthpiece may be sharp on their bars.
We do this with our young horses before they get started, so being bridled, wearing the bit awhile, is not a big deal, nothing to get excited about. We call it “mouthing” the horses because it is what our Grandfathers called it as they started young horses.
Seems to take the fun out of chomping on the bit, as their jaw gets tired. All but two horses we have done this with were very quiet in the mouth afterwards in any any work sessions. The two who were not, were exceptionally mouthy horses, a mother and son. They just seemed to need to lick or put lips on things when held, NEVER bit things. We gave them loosejaw bits, which allowed them to lift and drop the ported mouthpiece when they needed to stand quietly. Just gave them a “fidget” toy, they never moved feet or swung heads while standing for long (competitive carriage horses) times until their turn. Mare’s other sons did NOT do the fidget thing at all.
Your mare might just have never worn a bit except in work, so she plays with it waiting for more training things. May be a bit stressed, waiting for “next” thing. Never got tired to the point of just holding the bit quietly. S