The best explanation for what Bill observed is:
The water bottle crumpled as a result of the volume shrinking with the decrease in temperature.
When the water bottle was immersed in boiling water, the air inside the bottle expanded due to the heat. When Bill then transferred the bottle to cold water, the temperature of the air inside the bottle decreased, causing it to contract. This contraction led to a decrease in volume, which resulted in the crumpling of the bottle.