I guess I should ask a few questions, where are you standing when you take off the halter and put on the bridle and do you keep the halter on him, around his neck or take it off completely? You should be standing beside him not in front of him. And keeping the halter on till the bridle is on. I ride with a rope halter on (trail riding) so I just keep her tied till we are ready to go, she can't put her head down even if she wanted to. I tie to a ring above her head so she is tied up. The shoving is a sign of disrespect and I wouldn't let him get away with it. You may try backing him up and doing some yielding exercises when he does this just to let him know who is boss. Hope this helps, its just the way I do it I'm sure there are others.
"Until one has loved an animal, part of one's soul remains unawakened..."
- Anatole France