LJ is right, the bleach will react away within a few days. Don't need much, but you should do some for the same reason cities use sodium hypo-chlorate (bleach) for water treatment.
I solve the water storage problem (not for hurricanes, but anything/everything else) is to pump water from the well directly into large water storage tanks (800 to I think 1500 gallons), then use a pressure tank and small pump into the house. One is set up for gravity feed.
Even someone not on a well could purchase a large tank or two and have in the back yard or good sized garage. Lots of water even if no electricity is real peace of mind.
We’re looking into a solar well pump since it’s a bit too deep for a hand pump.
I never use milk jugs. The new ones they will never seal tight after the seal is broken. Besides possible contamination, if they tip over in your car you, have water all over the place. We use the gallon cranberry juice containers. They are sturdy, clear and seal tight. You may not have access to these in your area.
Reliance makes 7 gallon Aqua-tainers with a spigot and are BPA free. They will cost you less than buying 7 gallons of bottled city water.
If you want to put bleach or any other chemical in your water (like the cities do) that’s up to you. I don’t drink city water unless there is absolutely no other option available.
To your health!