Barometric pressure and bass

You read everywhere about drastic changes in barometric pressure
effecting bass behavior, because it affects the swim bladder, which is
very sensitive. This part I understand, at least in theory. What makes
me scratch my head is knowing that just by changing depth in water by
one foot exerts much more pressure on the fish than any change in air
pressure. It takes sensitive equipment to measure barometric pressure,
but even I can feel the difference in pressure of a few feet of water.
So I wonder?
1. Is it really the barometric pressure that affects bass, or some other
factor that happens at the same that we just haven't discovered?
2. If it really is that tiny change in pressure, wouldn't just a few
inches change in the lake level affect them the same way? (given that
they are staging to structure and not water surface)
3. Would fish in tidal areas, or anywhere that water levels change
quickly not be able to detect barometric pressure changes?

I think I sprained a muscle in my brain. How do you stetch out a brain
before giving it a workout?
Henry