Bridling or bitting up is not going to help you. If your horse is running through you in one bit, adding more 'pull' is just going to teach him how to keep ignoring your aids until you eventually run out of bit options. Go back to your basics. Lots of walk/trot/canter with transitions, and if he starts to rush or become flat, putting him to 'work' with some smaller circles, serpentines, bending exercises, lateral work, etc. may help him focus more and start to give him something to think about and will get him using his body correctly.