Bleach will kill bacteria. Vinegar will remove hard water deposites.
It's worth noting that most of the nasties are held in place by the hard water deposits. Get them out, and everything else comes out with them.
9% acidity vinegar is about $3/gallon around here, so I run a full pot at full strength every 6-12 months. The vinegar comes out brown, and the rinse water comes out clear. When we were on well water, I did it every month with similar results.
Have proper ventilation. One sniff of hot, high-strength vinegar is enough to be rather painful. I haven't noticed any long-term effects from several exposures, but I still open a window and/or wear a respirator when I'm close to it.
Bonus: put your shower head (and the aerator from the sink nozzle, and anything else with calcium deposits) in the pot of hot, dirty vinegar for 10 minutes, and it'll flow like new.