Keeping a white convertible top looking nice is a real PITA. I would suggest a mild soap and a soft-bristled scrub brush as a starting point. As you stated, don't use any harsh cleaners or bleach. Back before I restored my convertible, I tried all sorts of cleaners (including some kitchen abrasive type cleaners, eek) and could never get the top completely clean. I now have a new top, but know it will slowly get dirty.
Once you get the top clean, if it is still discolored there may not be much you can do about it, short of using a dye or something like SEM Color Coat.