my Sister said once she never washed her dishes before putting them into the dish washer. I asked her what she thought all those food particles did... disappear? there should be a filter or trap you must clean out if you do that. I always washed mine first. now the house i'm in has an old dish washer and i just wash my dishes by hand now.
septic tanks are tricky. i don't believe bleach is a good idea. i hope you find another alternative.