Storing such a weak solution distilled is better, however it's more normal to store as a 10% solution, and it all depends on how pure your tap water is if you don't use deionised or distilled water.
So you store it in 10% solution and then everytime you need to bleach you mix some of it to make a more dilute solution? The more dilute solution to you discard it after use or can it be saved for a prolonged time?
I have som very dilute solution I mixed a year ago and Im still using it. Is that a problem?