Remove dirt from the bell using a dust buster or hose at the end of a vacuum.
Remove any dirt that the vacuum did not pick up using a dry cloth.
Mix 1 gallon of warm water with two spoonfuls of mild soap in any sized bucket. Refrain from using soaps that are strongly scented.
Dip a clean cloth into the bowl of warm, soapy water and lightly scrub the bell. A toothbrush can be used to remove dirt that has yet to come off.
Rinse off the now dirty cloth. With clean, warm water, wipe down the bell and any remaining soapy residue.
Allow the bell to dry completely. This may take several hours.
Apply a small amount of plain clear wax onto the bronze and scrub in a circular motion with a new cloth. Some suggestions for wax purchase are Trewax, Johnson's Clear Paste Wax, Mohawk Blue Label Paste Wax and Renaissance Wax. Wax will help fight off oxidation which would otherwise result in the bronze turning green.