Let me add to Watermom: If your calcium hardness levels are low, you can use Cal-Hypo to chlorinate. Like bleach, this will NOT lower your pH but may even slightly raise, but will add calcium to your pool.
BTW, instead of bleach I use Liquid Chlorine. It's the same stuff, only stronger--12.5%, and comes in 5 gallon reusable containers. Add a reusable spigot (about $5) and 3 containers are the equal of 30 gallons of regular 5.25% bleach.