Why do ice crystals form from the top to the bottom of a bottle filled with supercooled water?

The water is supercooled,that is below 0°C . So density of water is probably not the issue. The hydrostatic pressure is also unlikely to be significant for a small bottle. If there were nucleation sites, supercooling would not have been possible.

The key issue is the necessity to disturb the water by giving it a "bang" to freeze it. This disturbance would be significant at the surface where there is a open surface. That is the most likely reason

Three possibilities:

1. The surface is free to flex, to ripple, and that can promote crystal nucleation. A ripple reflecting at the container surface is doubled in amplitude (by the reflection) locally.
2. There is contamination at the surface (floating specks?) that is introduced when a shock is applied to the container (dust dislodged and falling onto the supercooled liquid).
3. The bottom of the container is under higher pressure than the top, and pressure melts ice near the freezing point, in water. Nucleation under pressure is slower than nucleation near the surface.

An unobserved crystallization would make an ice crystal with lower density than the surrounding water, which would float to the top of the container; I'm assuming that isn't happening here.

Here's another possibility. When I've done this experiment myself, I've noticed that ice forms in the cap. I didn't need to apply a strong shock to get formation of ice—I merely needed to tip the bottle so that the supercooled water made contact with the ice crystal adhering to the top of the cap. We can't know without looking at the cap, but I think it's possible that the water in the bottle freezes from contact with ice crystals in cap, not due to the shock.