So I can only recommend bleaching and lightening be done by a professional who knows how to lighten hair with maximum respect for the condition of the hair. But if you are determined to do it at home the product I use in the salon is Proclere BlueFrosting gel lightener. I mix it with a 6% 20vol developer and process it as according to the manufacturer’s instructions.
Remember never to overlap your bleach onto the previously lightened hair and always tone afterwards with a good cool toner if you are going for that icy platinum. Most importantly use an intensive protein and moisture care regime that will put back some of the life the bleaching takes from the hair.