Bleach will tend to drop your iron out -- where it will either (a) drop to the bottom, (b) stain things, (c) come out on the filter, or (d) all 3. Filtering and vacuuming will then clear everything except the stains.
A 16' pool with 2.7' water depth holds about 4,000 gallons with a PF=30, so a gallon of 6% (check the %) PLAIN household bleach will add about about 15 ppm (0.5 lbs Cl2/gal of 6% bleach x 30). Adding a single large dose of bleach via, circulating it, and then letting it sit overnight may well drop it all as rust dust to the bottom of your pool. That's easy to clean up IF you have a way to vacuum.
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