Your intuition is correct, but a minor nit: bulbs aren't linear devices and don't have a fixed resistance. At low power, a bulb will look pretty close to a short circuit (it's just a piece of tungsten wire, after all). As power increases, the filament temperature rises and so does its resistance. This is why bulbs generally burn out when turning on - 170V across a mostly short circuit, with most of the resistance being in whatever section of the filament is most worn through, so most energy is dissipated at a single spot. poof!.