Bleach has a pretty short shelf life; can’t remember but IIRC it’s less than a year. It reverts back to salt or something; sorry I am not more specific. But I have opened a bottle of bleach years ago that I’d had around for a long time and it wasn’t bleach any more.
The survival-y websites usually discuss that and know the shelf life.
I have a Berkefeld water purifier plus good well water so I don’t worry about bleach.
Short term, use the bleach. Beyond six months use the water purification system.