I also ride an Appy. They are smart horses.
As the above folks said, it is a matter of having her reeducated as to the meaning of the bit, which means that you might need to do a little reeducating yourself to that. I mean no insult, but rather somewhere along the line she has gotten dull to the meaning of the bit , and you will have to be sharp about it to create a new sensitivity in her.
That means that you never pull unless you have to, and you never let her lean on the rein or meet your pull (pressure maybe better word) in a way that creates a stalemate tug of war.
YOu use a lot of bending to break up that tug of war. YOu meet her pull , if she insists on it, but you put in an ounce more 'til she gives. And when she does you must be sharp to give her a good release. This waiting for HER to give and then you giving even bigger is what builds in the new response to the rein.
Also, don't hold onto the rein when you are just standing there . Use it if you need to stop , get the stop and then release. It's like riding the brakes; it will wear them out.
There's a whole lot more to it but there are ways to get a horse softer to the bit, but you have to be really aware of how you are using it, and very consistent.