putting pressure on the poll is fine if you have a pony and are a good 5'9 + anyway.
you get to something bigger, or something that already has its head firmly in the rafters as soon as you enter the stable with the bridle, unless you have a step ladder (which you appreciate isnt the best considering said horse could fly around the box trying to get away from you again) its not gonna happen.
(can you tell im dealing with this issue on another horse i ride atm)
reins around neck, then hide bridle. stand just to side of head and ask him to come down for a stroke. give him a rub all over his face (he likes it alot) then work up to ears. once you know he is more settled, put bridle into clear view (with bit already undone at one side) and put it on as a normal head collar. fasten throatlash and noseband. (all done while chatting calmly and quietly been purposeful and not faffing but not rushing either) then hand over top of nose with little finger just near corner of mouth to guide bit in. free hand around front of mouth (with bit in) thumb through the ring once lined up hand round to side and slide bit in as normal. again not rushing so you bash teeth, but you need to be swift before he shuts his mouth and trys to do a bunk
fasten up, praise then ride.
when finished- undo throatlash and noseband. leave reins over neck.
then undo bit but hold it in place.
take hold of top of bridle (loop hand under neck) in one hand, slide bit out first (slowly, important not to catch teeth) praise verbally then take rest of smoothly.
its works, and after a while you can stop going through all this because they forget the issue in the first place.
good luck