Is it possible for a bulb to behave like an inductor?
Only ideal (theoretical) components have a single behavior. Real components always have multiple behavior. The secondary behavior is usually far less significant. In the case of an incandescent bulb, it is primarily a resistor, but a coil of tungsten will have some value of inductance as well. At AC power frequency, 50 or 60 Hz, the inductance will be insignificant, but if you use a bulb for a load in a radio frequency circuit, the inductance might be significant.