It is a well known fact that stuff does not function the same way in space as it does on Earth. As a consequence, results we get in response to our actions are quite different. How does this apply in case of firing a gun, though? Whether it is a rifle you are carrying or a water pistol, shooting it on Moon would increase the likelihood of the shot coming back to hit you.
This largely depends on where a person is firing the gun. Astronauts on the International Space Station are of the view that one is required to attain a speed of atleast 5 miles per second prior to reaching the point when the speed of one falling matches that of the Earth curving away. As astronauts continue to fall to Earth, the Earth falls away from them at the same pace.
Since the Moon is smaller in size, it has lesser gravitational pull. Anything that orbits the Moon would not need to be in motion at such a significant velocity. In case of shooting a gun in the center of space, the bullet would vanish in darkness as the galaxies speed away. Afterall, they travel at nearly 124 miles per second whereas a bullet merely achieves 0.62 miles per second.