Oftentimes, at least in the United States, people use creams for the opposite purpose (to make themselves look more tanned), so I'm not sure we even have a word for it in AE. Then again, I'm not too knowledgeable on spa centers.
I've never heard the term "white bath," so if this process exists here, it must have another name, and I'm afraid that I don't know what the name might be. There are "skin lightening" creams and lotions that are used to treat things like freckles, hyperpigmentation, or liver spots.
I guess you'd call it a "skin-lightening treatment".
I am aware that in Asian cultures (Asia, India, ~Middle East), light skin is perceived as better or prettier or of a higher class, and as such, there have been many forms of skin lightening treatments over the years. However, to my knowledge, this obsession does not currently exist outside of Asia, India, and maybe the Middle East.