I'm short, too, so find it easier to hold the bridle in my right hand, up by the ears and away from the eyes, let the bit swing *below* the chin and bring it up with my left hand from below the chin. This helps keep their head inside the bridle somewhat even if they toss their head, so they never really succeed in getting away from the bridle. This works better for me than bringing the bit toward the horse from in front of their face; I saw one of the clinicians do it this way and it's easier for me.
To get mine started off on the right foot with bridling, I smeared syrup (or dribbled Dr. Pepper) on the bit and they scarfed it up like candy. If you don't mind the potential mess, this is an old-timers trick that might work if your guy is food-oriented.