I haven't finished Z for Zachariah yet, but is there radiation in the water and an intense scrubbing will protect you from it? Why does Margot Robbie wash Chiwetel Ejiofor in Z for Zachariah?
Well, in answer to the first part: Yes, the water in which John Loomis (Chiwetel Ejiofor) was swimming/bathing when Ann Burden (Margot Robbie) came up to him is irradiated. Without getting too "spoilery", the area in which Ann lives seems to be one of very few (if not the only) radiation-free zones at the time of the story. However, the water in which John was swimming comes from outside of that area (the waterfall).
As for the beneficial effects of the bath, I think the link to the "Silkwood Shower" reference by @Will-Feldman is probably as good an explanation as any. Try to get as much of the irradiated water off of the body as possible. John is obviously still going to be affected by his exposure, but there's no reason to allow more of the radiation to seep in if it can be prevented.