Well, she is a trained horse, apparently, so I don't think she needs that colt bit intro of having a bit left in her mouth to eat
Some horses get bad about being bridled, simply because someone has allowed them to, thus you go back and work on basics, such as having the ability to ask er to lower her head, versus raising it, when go go to bridle her.
The finger is good, but then wait for the horse to open her mouth herself to accept the bit, while she continues to give her head.
If instead you allow her to raise her head, clamp her jaw, even that finger is not going to do much.
Once she accpects the bit, then gently place the headstall, over her ears.
When you take the bridle off, do it in reverse,. Ask her to lower her head, slip brow band form behind ears, and hold it, waiting for her to drop that bit, versus pulling it out
How is she once bridled? Happy, no fussing with that bit, of mouthing it , chomping on it, getting tongue over it, ect? If she does the latter, then she does need to learn to carry a bit. I like to do it while lunging a green horse, just tying those reins back loosely and lunging off of the halter under the bridle
I used to let them carry it and eat with it, but now no longer do so. Eventually, I want the horse to work with that bit, and not eat with it, having a quiet and relaxed mouth.