The bulb probably does not have a switching power supply. Rather, it probably has a capacitive dropper, with U1 being a current regulator chip. Check out Big Clive on YouTube - has had done autopsies on dozens of bulbs, complete with schematic diagrams and clear explanations of how each bulb works. If you really want to understand how LED bulbs work, check out Clive's videos.
A capacitive dropper circuit is similar to using a series resistor to drop voltage, but a capacitor's reactance (rather than the resistance of a resistor) is the key element. Little power is lost in a capacitive dropper.