Unless I am forgetting something the PBW will do everything you need, the bleach is an unnecessary step, but I would suggest pumping PBW solution through it for only a few minutes.
Pump PBW solution for 1-5 minutes, let sit 15-20 minutes, pump 1-5, wait 15-20...cycle like this until the PBW solution has been in the pump a minimum of 1 hour [for the first cleaning, for subsequent cleanings 30 minutes should be fine]. Then rinse by pumping some water, then a Star San mix for total contact time of 5 minutes and everything should be golden [as in good, not the color, LOL].