You said bulb, a bike headlight bulb is 2.4w. what is the hub output?

typically a bike generator is 3w, with an 0.6w bulb rail light and a 2.4w headlight bulb,

one burns out the other is overpowered..

Now, LED lights get an IC, with a rectifier (AC to DC)
and an overvoltage regulator in the circuit..