This thread is full of
Water softeners don't remove bacteria, they remove the hardness/calcium & magnesium. Salt is required for this as its an even ion exchange.
Salt less systems are a scam and don't work and will still give you build up throughout the house.
If its city water it's already chlorinated, therefore no bacteria. Unless you're in Toledo then there's that toxin issue
- which chlorine doesn't fix either. High levels of chlorine will kill the algae (Cyanobacteria) but will NOT remove/kill the toxin (microsystin) it produces.
I don't know how a plumber can tell you that he tested for bacteria, this needs to be done in a lab.
If you're on well water and do in fact have a bacteria issue, you need a chlorination, ozone or even better yet a UV setup.
ETA - see you're on well water. You could infact have iron bacteria and this will cause an oily slick in the back of the toliet and could lead to other slimy areas.
Do you have any odors, particularly sulphur? (The rotten egg smell)