Teach him to lower his head, yes, but here's a trick I'm going to share.
If you don't already have a rope halter, go get one. Leave the halter on as you go to apply his bridle. If he puts his head up, gently ask for it down. Do not put the bridle on until you can approach him with it without him pulling his head up. Slide the bridle on, undo the rope halter. You will then put the top of the noseband into the horse's mouth just like a bit. Work the halter round the bit, and slide it underneath the bit. Then pull it out. Voila! You need a rope halter, a nylon halter won't work.
This works because you can keep influencing his head down with the halter at the same time. :)