I am in no ways a professional, but some things in this article really seem to make sense in beginning to soften a horse's mouth. http://www.hokana.com/article14.htm
A horse doesn't like pain from the bit.. but at times they'll plow through it.
My trainer told me to comb the reins to get him to open his jaw and thus be more soft. You can practice at the stop, walk, trot, and even canter (I haven't gotten that far..)
But beware, it feels good to your horse so don't drill it into their brain or they will become addicts!!! :P Kind of joking, but also serious.
Also, try groundwork.. lunging in the bridle, attatch the line to the bit and instead of pulling hard to get them to change speeds, do little half halts until you get a response.
Everything you do on the ground transfers to saddle and makes things a lot less confusing and frustrating for you and your horse.
Once again, not a professional.. just a horse woman!