A stronger bit will be a quick fix, but its not a real fix. That is not adjusting the behavior of the horse, it is just forcing the horse to behave a certain way. A better approach is to change the attitude of the horse, but unfortunately that takes some time and effort. I would advise leading exercises. This is an indirect method that gets the horse to stop having an attitude. Exercises you work on while on the ground will translate direclty into the saddle. So teach the horse to stop on a dime when on the ground. Read this free article for some tips on leading. Also, spend some time working on teaching the horse to pay attention to you. This will make any horse ride lighter and more responsive. Then watch this video on getting your horse to lean forward and backward without moving his feet.

David
http://gentlenaturalhorseman.blogspot.com/