The copper can be easily polished with a copper cleaner (brand names such as Brasso) or with a simple home recipe of lemon or lime juice and baking soda.
Steps:
Cut a small lime in half and dip it in some baking soda. Rub the lime with the baking soda onto the oxidized parts of the copper and voila - the bronze colour returns. The baking soda is a natural exfoliant and helps to lift the oxidized particles.
There are many other ways to clean copper, but you will always need some type of natural acid to achieve this. Vinegar and tamarind are often used in combination with baking soda.
Please don't put copper into the dish washer or fill the bottle with juices, sodas or hot beverages. Milk and copper cause a toxic reaction and should always be avoided.