Vesta Moves! Images of the asteroid Vesta taken on 20-07-11 and 21-07-11 at 11:30 pm using a Canon IXUS at 3.0 x optical zoom and ASA 400 for 15 seconds exposure (hence the trailing, click to embiggen).
The Asteroid Vesta is currently bright enogh to see with the unaided eye .. if you're somewhere really dark, my backyard is not. However, it's really obvious in binoculars, and a simple unguided 15 second exposure with my "point and shoot" digital camera was good enough to pick it up and its movement over successive days.
Why don't you try it?