The best description of what happens to the temperature of each after the bottle of liquid water is placed into the tub of ice is: The temperature of the ice increases, while the temperature of the water decreases.
When the warmer water is placed into the ice, heat will transfer from the water to the ice, causing the water's temperature to decrease while the ice absorbs heat, causing its temperature to increase. Over time, if enough heat is absorbed, the ice may begin to melt.