There are many substances that will kill plants, and almost all of them shouldn’t be used in your garden. Bleach (sodium hypochlorite) is one of those things you should avoid. Yes, it will kill or injure weeds, but also any other plant, animal, fungi, or bacteria it comes into contact with. Besides the immediate corrosive effect on living organisms and organic matter, bleach is quite alkaline (pH 11), so it will negatively affect the pH of your soil.

If you’re looking for an environmentally-benign alternative to glyphosate (Roundup®, etc.), you’ve picked one that’s much, much worse and totally indiscriminate about which lifeform it destroys. If you want to keep chemicals out of your garden, pull, hoe, or till grass and weeds, or smother them with mulch.