BTW, I have bridled my horse over a halter. Then you just have to undo the bridle straps individually to take the halter off. My horse was reluctant to take the bit and bridle and she would toss her head all over the place. Keeping the halter on worked, although it was a bit of work. Anyway, I had her teeth floated...no more reluctance and no more bridling over the halter.
If you're able to before you tack him up, groom him exactly like you do at home on a regular day. Even if he's squeaky clean and show-shined. Use his brushes from home (you can clean them if they're dirty so they wont mess his coat) and groom him the same as he's used to. This will help him to relax and realize that everything you're doing is the same as usual, even if his surroundings are different. Horses are like human babies, they thrive on routine.
I agree with the halter over the neck that everyone else has said.
You could also practise at home. Bridle him in places you don't normally bridle him....the outdoor arena. The indoor arena. Go for a hack with the bridle over a halter and take it off and put it back on while out on the trail.
The biggest thing is not to be nervous about it, because he is most likely picking up on it, which is why he isn't being the most cooperative at shows.
The show went great! I used the neck collar it was a life saver! Here are some pics from the show.....(btw he was awesome for his second show! Very calm yet we did not place since it was points and we just joined. The last show of the season :) )
Yeh id say either just put it on over the halter then un doo it, or slip the nose out so its just around the necks than fasten the bridle and take halter off. I had to do that for a while, and still do when im out and about :)