Steve,
If you add the bleach every night and then run the filter till morning the chlorine will be distrubuted throughout the water. As long as you aren't shocking the pool, i.e. dumping 4 jugs of chlorox in, it should be fine for them to go in the following morning. Just use the bleachcalc so you aren't dosing past target ppm.

** Also, I see from your sig that you use the Nature2... search for Nature 2 and read through the posts... you may have gotten 'pool stored' on that one too. Don't replace the cartridge next time.