You hear this saying all the time. Sometimes talking about things not related to horses. If a person or animal "has the bit between their teeth" then they're the one in control of the situation.
Okay. The bit sits in a gap between the teeth (caused by the fact that horses don't have premolars). If the horse stops responding to the bit, we may say it 'has the bit between its teeth' - but is this literal?
Actually? Very few horses can get the bit between the molars. It involves opening the mouth very wide and then lifting the bit up with the tongue. It's not impossible, but it's highly unusual. Instead, the horse may lift its head into a position (above the bit, as discussed before) such that when the rider pulls the reins the bit pulls against the teeth rather than the gums. Or, the horse may lift the bit with its tongue, tense its lips against the bit, and perform other maneuvers to reduce the bit action.
But "between the teeth" does not mean the horse literally has the bit between its molars in most cases. It simply means it is not responding to the action of the bit.