Step 34: In operation: Disinfect with chlorine bleach.
The active ingredient in chlorine bleach is sodium hypochlorite. It's a powerful disinfectant that self-decomposes into water and salt. Age, sunlight, warmth, and graywater impurities (including playa dust) all increase the rate of decomposition, and eventually exhaust the disinfecting power. So, make sure your bleach is newly purchased, not left over from last year. The following rule of thumb will help compensate for other uncertainties.
The No-measure Rule of Thumb for Disinfecting: Follow Your Nose
Loosen the cap of your bleach jug one-half turn: no farther, or it may come off. While using your thumb to restrain the cap, invert the jug over the tray, or over your container of incoming graywater, and dribble for about two seconds per gallon. In half an hour or so, sniff the tray. If it doesn't have a faint chlorine aroma, dribble more bleach into the tray, about five seconds' worth. Check the aroma again, in another half hour. Repeat as needed; morning and evening at least.
Graywater left to stand untreated eventually becomes blackwater as microbial populations increase. People who haul out all their graywater at the end of the week have worse stuff to manage than you do, unless they also treat it periodically with bleach. They also have containers that can't be reused safely for anything else.
When buying chlorine bleach, check the label for the concentration of sodium hypochlorite. Concentrated Clorox Regular Bleach has about 9%; If another brand has 6%, it should cost two-thirds as much and you'll need to add 1.5 times as much. Scented products are always lower in hypochlorite. Bleach has a limited shelf life, and this year's leftover jug won't last til next year.
Disclaimer: I am not an expert, but I have corresponded with an expert at Clorox Corp. Following the guidelines above is not guaranteed to fully disinfect your water. I will update this step as I gain new information.