I would not use bleach on china or porcelain of course, but I have used bleach cleaner on inexpensive heavy mugs, with great results. Try it on a cheap mug that you do not really care about to see how it work, dilute the bleach cleaner first. Not straight bleach, but something like soft scrub with bleach or another non abrasive bleach cleanser. Rinse and rinse and rinse well.
Happy thanksgiving.
Happy thanksgiving.