Chlorine Bleach Method
Prepare your sink for bleaching by ridding it of soap scum and buildup by cleaning it with vinegar. Pour vinegar on the sides of the sink, let it sit and wipe it clean with a sponge. Use the scrubber side to take off any stubborn buildup. Be sure to rinse the sink out thoroughly because mixing vinegar and bleach is hazardous.
Fill your sink with water, add 1 cup of chlorine bleach and allow it to sit. If you have issues with the smell of chlorine bleach, dampen your sink and use a scouring powder instead. Coat the sink with the scouring paste and allow it to sit for several hours.
Empty or rinse out your sink. It should be sparkling white.
Clean your sink out with vinegar to rid it of any soapy residue or other buildup. Use a scrubber sponge to loosen up the stubborn stains, re-applying the vinegar if necessary.
Mix an oxygen bleach product with water and following the directions on the package. Soak a couple of old rags in the mixture and place them on the bottom of your sink.
Leave the rags for several hours. Lift the rag to check and see how it is doing. If it hasn't whitened enough to your liking, re-soak the rags and apply again. Take out the rags and place them in the wash. Rinse out the sink.