Why has Earth been bombarded more frequently by asteroids than the moon? Why are impact craters more commonly visible on the moon than they are on Earth?

Well I'm no expert, but earth is hit more than the moon because we are a larger planet. We have a larger and stronger gravity field, thus pulling more asteroids to the earth. The second part of your question can be answered in the same way. The size of Earth dwarfs the craters created when asteroids strike the surface. Not to mention that 90% of the asteroids we are bombarded with burn up before they make contact. Another reason for less visible craters is simply life. The moon has no sentient life. The life on earth commonly covers these craters, such as vegetation growing in the soil where an asteroid crashed into the Earth.