If you have a chrome bridge, you can remove rust/oxidation by doing the following:
Dip a piece of aluminum foil in water (15cm square or 6" square) fold it over a couple of times and polish/rub the chrome with the aluminum foil.
Keep dipping the aluminum foil in water as needed and change to another piece when one wears out. You'll notice a blackish paste develop as you polish, this is good, it means you're removing the oxidation and rust.
When all the rust is gone, rinse with water and dry everything off. To make sure you get all the water out you can use 99% rubbing alcohol to evaporate the remaining moisture.
*Aluminum is softer than chrome and steel so it will not scratch them. Works great for faucets, door knobs, bumpers, etc. as well