Heck, even if he fired multiple rounds it could be dismissed as Clark suddenly having a bad dream, or a restless period of sleep.
A sharp shooter tried to shoot Batman - he had him clear in his sights - and the bullet missed him. The shooter didn't jump to the conclusion that Batman is also Superman
In the Lois & Clark series, Intergang (I think) tried to tag Clark with radioactive tracer via a 'bug', but each time they tried it the injector on the 'bug' broke. They just figured they were hitting his watch or something else, not that he was invulnerable.