look man if you wanna attach lighting man, just add your motor asynchronous generator thing to get AC. Screw the damn battery and bridge rectifier...
Even if you added a rectifier, the wave form would not be pure DC, it would be halfwave or fullwave DC. You would need a filter inductor and capacitor, in which the size of capacitor can be calculated by the formula: If you cant do the formula calculations, then i would say dont bother, but if you can, then go for the AC to DC conversion.
For example: You have a 120 volt AC generated from dynamo and then it goes to 120 full wave DC after the rectifer and you want the ripple to be half a volt so you can get pure DC. That means 119.5 120.5 cycle back and forth which is close enough to pure DC. A switching power supply might have a ripple of 0.01 volts. Who knows without a oscilliscope!!!! Then plug in the current draw, and the frequency of the AC being generated, probably 60hz in households, but IDK what your dynamo is, you have to look it up or calculate it from a formula.
Then solve for C, which is capacitance in Farads. That will give you the answer to size for your rectifier circuit.
The inductor you could pass up on, but the capacitor would be necessary.
Easiest thing is f*** it and add some generic non DC lights, like some flourescent house lighting and jery rig it for your bike...
Some commentors said with AC it would be on and off the lights. No, it would be going on and off 3600 times a minute and not abruptly and your eyes would never never never never never never never never notice,
Also I hate toggle switches. They break. I once used one as a cut off and it died after like 2 weeks. Please use generic 15 amp houshold switches. They are cheaper, around 1 dollar, and can handle much more juice and longevity. Circuit breakers can also be used as a switch too and work great