Thanks for your question. There are risks involved with using bleach though I'm not sure how to quantify them. It would make sense that these risks increase with the number of repeated applications, strength of the bleach being used, etc. More importantly, there are excellent medications for the treatment of ringworm. Typically I treat ringworm (which is really a fungus) with a topical antifungal creme. Because it is on the skin, the relative absorption into the body is low, making it a safe medication. It is also cheap. As important as treatment is prevention of another infection. Here is an article I found online about it:
Sometimes I do prefer home remedies to medical ones. However, when the home remedy has potential side effects, and the medical treatment is effective, safe, and inexpensive, I go with the medical remedy.
Hope this helps,