My BO's daughter's horse was use to turning around in a larger trailer and walking off straight. He was loaded into a smaller trailer one day. After arriving at his destination, his head was untied... And he turned right around to walk out, only this time there wasn't enough room. He got struck, struggled, and fell. It took two years to get him over the trailer issues this incident instilled on him. Moral of the story: if your horse always walks off a trailer after turning, he will not be use to backing off a trailer. Some trailers you must back out of. It's am important skill to learn.
My mare had the exact
same problem with the bridge. She walked forwards fine, stood there, but wouldn't back. I back through everything I can, so naturally I ask for a back and find a horse rooted to the spot.
My horse's back on the ground was great. I could back her with no halter pressure; I just stepped forward her and said "back". I assume your mare's back on the ground is very good...
I got a dressage whip, stood in front of her (but slightly to the side; never know when a horse decides it's going to go forwards), and tapped her between the frong legs (not hard; just enough to be annoying) while asking normally for a back. I kept this up until I got a single, shaking step back. JACKPOT, reward! Repeat until satisfied, praising each step back and pausing after each backward step to allow "thinking" and calming down time.