Not sure about this, but what if when you pull the headstall over the ears, you hold the bit in place with one hand. Then , when the headstall is free of the ears and well down the face, you kind of wiggle the bit in your holding hand a little, to encourage her to hold it with her tongue, then let go of it. Theoretically, she will hold it with her mouth and eventually spit it out on her own . It's just slightly different from having the bit drop down on it's own AS you pull the headstall over her ears. I have no idea if it will feel better to her or not.