To dream of a light bulb represents an idea. It may also reflect your awareness of whether or not an idea is working. Trying light bulbs in a lamp may reflect new ideas you are experimenting with. Giving different methods a shot and watching the results. Approaching a situation from a new direction.
To dream of a burned out light bulb represents feeling ineffective or your awareness that an idea doesn't work. Feel like you are out of ideas or have nothing to offer.