I followed the advice of a mechanic on YouTube and use Blue Dawn liquid detergent in warm water with a wash cloth, and he was right, the dirt came off in no time and I was finished with both bars in about 6 minutes tops!

The blue dawn works well because other colors tend to leave a residue on white. Same theory for using products on grey hair, use either clear white or blue and you'll always sparkle. (Month 3 of the great grey experiment)