How much bleach are you using? You only need to use a little bit of it for doing your dishes, if that is what you wish to do. I dont use any bleach for dishes, but understand that some may like to such as yourself.
Now for laundry I do use bleach and we also have a septic tank and I haven't had any problems. Did the tank guy say to use Rid X? If you google this issue you may find some solutions.