This is hard to determine without considering a specific circuit but generally this type of circuit should be stabilized with a regulated power supply. If the voltage from the power supply to the circuit changes, the intensity with which the bulb burns could be effected skewing the range of brightness for which the circuit is �designed�. Power supply variations could also effect the average current through the photo resistor for a given illumination. In combination these variations would not necessarily be complimentary and parallel leading to ambiguities in the circuits output.
Power does not affect resistance. Resistance affects power. For a given voltage, the resistance of the bulb in your circuit will determine the power used, since the power will be in accordance with the formula P = V�/R