How can I reduce bruising on my foot after a sprain?

You can't . Bruising is a normal reaction after an injury. Whenever an injury occurs you break small blood vessels which leak out blood into the area and cause bruising.
Brusing. If the brusing is from an injury it may be very difficult to do. You see when you injure yourself, there usually is bleeding at the site under the skin. This is the cause of brusing. You may be able to decrease the brusing and swelling by following simple steps that are tried and true such as r.I.C.E. = rest, ice, compression, elevation.