You are 100% correct about bleach being a good way to purify water. But a lot of people don't know that the bleach you buy in the store is only good for about 6 months. The chemical bleach is made from is cheap. For about $25 you can get enough to last a lifetime. But it is VERY IMPORTANT to store it correctly.

Several months ago, I wrote a very detailed article on what to buy, where to buy it, how to mix it to make bleach and how to safely store it for long term use if you are interested. https://steemit.com/foraging/@fernowl13/purifying-water-with-calcium-hypochlorite