Since the ring pulls people and twists them based on their own personal power and ambition, its power very much depends on the stature of the bearer. Bilbo saw its purpose to be only to hide from people (like the Sackville Bagginses) he didn't want to see. Even when in the end it corrupted him, it was through simple lust for the thing. In the end he coveted the Ring itself, not the power over people he could have gained with it. Very similar to Gollum.
Frodo, we can't talk about yet...