Going to a harsher bit will only put a band-aid over the problem.
I would put her in a simple snaffle or french link (depending on her mouth conformation, I personally prefer double jointed bits, as do most horses, but some prefer a mullen mouth or single joint) and fix the hole that is in the horse's training.
Are her teeth okay? Does her saddle fit? Does her bridle fit?
Please have a professional assess this. Unless you are an equine dentist or professional saddle fitter, chances are you can't just eyeball these things.
You could switch to a harsher bit... and mask the problem, for now... then problems will arise later on, and you'll have to switch bits again... and again... and again. Turning to a harsher bit is a quick fix, it doesn't solve the problem.