If you are falling off to the left, then your horse is logically always spooking or spinning to the right. Your horse is likely looking left and falling right.
You could try keeping a bit of flexion or shoulder fore to the right which will weight her to the left and make it harder to bulge right.
I agree there is a big difference between horses that take you with them when they spook, and horses that get you off.
My horse as a kid had quite a big spook but I never came off. I did hop off and hold her if I could see she was about to lose her mind because of a city bus pulling up with hissing breaks or similar.
My current horse is very brave, and the few big spooks she’s had, she had clearly no intent to get me off.
A few years ago I rode an older mare that was fantastic in the arena but would do a kind of slow motion spook and spin on trails. I made sure to ride her with a bit of connection between leg and hand. She always spun left.
I do find that my teen reflexes still kick in, which is drop your leg, sit back and in, raise your hands.