If you can flake the coating off with your finger nail, this is more than a Patina. Patina is a chemical reaction with the bronze that provides a protective coating. It is usually an oxide of the copper and tin in the bronze. If the coating flakes off, the chemical reaction went much deeper than the bell surfance and has damaged the bell with deeper pitting. The bell may have been subjected to an acid bath or repeated exposure to acid rain. Sulfuric acid reacts with the copper to cause a blue Copper Sulfate. It will react with the nickel in the bell to cause a green salt Nickel Sulfate. Some salts of copper are rich green in color (Malachite Green). Perhaps the bell was painted and the flaking is from the paint. In any event, if it flakes, it cannot be restored to its natural bronze state without an expensive electrolytic process. It should be removed with a detergeant, water, and a bronze wire brush. Some use vinegar and salt with the brush.
Harry Long, MD