Why does filling a plastic bottle with cold water cause moisture on the outside of bottle?

Condensation

When you fill a plastic bottle with cold water, the warm air in the room condenses on the cold surface of the bottle. This is because the water vapor in the air turns into liquid water when it comes into contact with the cold surface of the bottle. The amount of moisture that condenses on the bottle will depend on the temperature of the water and the temperature and humidity of the room.