@scoop Bleach (full strength) is pretty corrosive and I'm pretty sure it would eventually damage the finish. If you look at the slides, Dr Honda gave a range of choices for your showerhead like alcohol and boiling.
My pulmonologist and I have a slight disagreement on this issue - I turned up my water heater, give the showerhead an occasional scrub with detergent and a brush, and call it "good enough." She thinks I should replace it every six months.
If you do bleach it, just do it before laundry day, throw it in the washer with a load of bleachable whites. Or use it to bleach toilets or the kitchen sink. Or wash it down the drain. Putting bleach down the drain is not recommended if you are on a septic system - it damages the bacteria that digests the waste.

@scoop, Does your own experience prove that it is enough? I am doing the same. So far so good. Keep my fingers crossed. But I totally understand, with this disease we will never be fully confident no matter what we do. It is sad, isn't it?
Best!
Ling