False.
The pressure at the bottom of a bottle filled with water is not zero. It's influenced by the weight of the water above it. The pressure at the bottom of a liquid column is determined by the depth of the liquid and the density of the liquid.
The deeper you go into the liquid, the higher the pressure due to the weight of the liquid above that point. So, the pressure at the bottom of a bottle filled with water is nonzero and increases with the depth of the water.