pump on/off when adding bleach

Definitely pump on. With any chemical (In my case mostly bleach and MA) I also go through the extra step of diluting in a 5 gallon bucket of water before adding to the pool to avoid a concentrated slug in any one spot. If I need to add both, I do them in separate bucket loads.
 
If you've got multiple returns in the pool, then adding the chemical slowly over a return flow in the deep end works really well since it has a lot of volume of water in which to dilute quickly, it has floor drains and/or skimmer to get back to the pump, and it then gets distributed to other areas of the pool via returns. If the chemical is relatively innocuous such as baking soda, then adding it to the skimmer to have it come out the returns also works well, but you definitely don't want to do that with acid (with chlorinating liquid or bleach I personally avoid that except on occasion, but we haven't seen reports of it being a problem).
 
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