The force of your lungs is weak compared to the force of the blow dryer. I do not think you dislodge many bacteria from surfaces just by breathing.
how about when you flush or the toilet self flushes and you are in the public stall fixing your clothes? do you breath in at all during that time?
I read many years ago its been shown particles can be dispersed up to 6 ft away when a toilet flushes.
People keep all sorts of stuff right above or beside toilets on bathroom counters and don’t bother shutting the lid. They don’t seem to realize toilets come with lids for a reason. I think public ones should have lids too.