Bit isn't necessarily the thing that will solve the problem.
Maybe try lunging in passoa and just click the ends between horse's legs. This will encourage the horse to lower their head.
When youre riding the horse you can try something I am using when riding a hollow horse or nervous horse with its head up which is a triangle system. So instead of having my hands above horses wither i put them wider and lower and by pulling and realising one and another (remember about the inside leg to support) i encourage them to relax and stretch down. You need to rememeber to be relaxed and patient so they can feel your positive energy. Reins can be lose not necessarily tense. You can short them and be firmer if the horse is not giving in.
Also pole work and cavaletti can be helpful to work on those muscles ;) ;)