Having their teeth floated is a procedure done by either an equine dentist or a vet. It's when any sharp edges on a horse's teeth are filed flat. The constant chewing motion that a horse does can affect a horse's mouth and sometimes wares down one side more than the other. If she is 10 years old, and never had her teeth floated, this very well could be the reason why she opens her mouth and avoids the bit. Some horse's need their teeth floated every year or every other year.
If ever my horse is acting up, avoiding the bit or just "off" for any reason, I ALWAYS check my tack first. A lot of times there is something pinching a horse, or digging into him. Think of a thorn being stuck in the bottom of your foot. It hurts, and you do whatever you can to avoid the pain.
So if her teeth are bothering her, and putting pressure on the bit in her mouth hurts her, she's going to open her mouth and avoid the bit as much as possible. She could also have her wolf teeth that some horses develop. Those teeth interfere with where the bit sits and if the bit hits the tooth, it hurts.
There isn't anything wrong with the type of bit that you are using. But in combination with that type of noseband, it's hindering the movement of the bit and you aren't getting the full function of the bit.
My horse hates that type of bit, but she works well in a simple O-ring snaffle. What does the mouthpiece look like? Is it twisted or smooth?