Why is it unlikely that bathroom smells can pose health risks?
Mostly, what you're smelling are volatile small molecules: stuff like butyrate, indole, mercaptans, hydrogen sulfide, etc. These molecules are thousands of times smaller than even the smallest pathogens, being measured in Angstrom vs. nanometer scales. Pathogens are just too large to be actually volatile, in the sense of freely escaping into the air. And fortunately, these volatile organics are not nearly as reactive as something like chlorine gas. (If they were, imagine the damage they would do, at a much higher concentration, to the person they were just inside.)

Now, if someone had literally just projectile-vomited (or if excreta were churned around, e.g., by flushing), it's possible that a very small pathogen like norovirus could spray outwards in an aerosol. Since norovirus has a very small infectious dose (on the orders of tens of viral particles) this could be enough to make you sick, and indeed, aerosols have been implicated in norovirus transmission, though it's not that common. But the smell would remain long after any viral particles in aerosols had settled down onto surfaces.