There are a couple of things you have to keep in mind: you hold a living thing in your hand, something that is easily pained if the bit acts on the bars of the mouth. Secondly, the mouth is only as connected and the balance only as good as the hand that horse it; so the rider must have a good seat and some basic balance before the horse will trust it. The rider should be aligned ear/shoulder/hip/back of heel, the upper arm should be vertical (serve as part of the trunk) and there should be a straight line from the elbow to the horse's mouth, and the thumbs the highest point, and the hand must be softy closed. No rigidity.
So, as to the horse: It should have its head up, its neck lifted and arced, the nose in front of the vertical. I think you are telling me that the horse is too high/inverted/'above the bit'. Why does it do this? The rider can be out of balance, the hand fixed too low/at the withers which can cause pain in the mouth, so it inverts to escape the pain (some horses curl instead). So, how to change things. If you take lessons there are a number of things which will assist in proper bit acceptance. Work in hand can help educate the mouth, work on the most basic of figures (a circle) will help (because lateral flexibility leads to longitudinal flexion/bit acceptance), adding energy will help. ALL riders need to work on develop the best balance/timing of aids that they can (so they need eyes on the ground). On a curved line keep the inside rein a little higher can help prevent pain on the bars, and funnel the horse into a better connection.