Pump run time?

I run mine 6 hours or so a day on average and it's a small pool. I run the pump around 4 hours at night after adding chlorine (I also brush the pool), then a couple hours during the day. I don't think you have to wait more than 30 minutes to an hour to test if you want to make sure the chlorine you added hit the target you were shooting for.
 
To make sure we address your specific question, the following is verbatim from the Pool School - Recommended Pool Chemicals

Bleach should be added to the pool by pouring slowly in front of a return jet with the pump running. You should pour slowly enough that pouring an entire jug takes more than one minute, preferably two minutes. Leave the pump running for at least 30 minutes after adding bleach.
 
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