Diluting 4 % NaOCl to get a 1 % solution
There is a simple dilution formula: $\mathrm{C_iV_i=C_fV_f}$, which is valid for all concentration units. The "i" and "f" indicate initial and final concentrations or volumes.

Using this formula, you can see that you don't need to prepare buckets full of 1% bleach. All you need to decide is what should be your final volume and final concentration.

As you highlighted, the issue, you cannot prepare a 1% solution and expect it to last for a day. It is better to prepare on need basis. The stabilizer in bleach is sodium hydroxide itself. Upon dilution, of course the base is also diluted and the pH is reduced. 

One can look at the distribution diagram of "bleach" as a function of pH (yes this is from a Handbook of Surfactant. It is a 4000 paged volume- books are still useful)