I've used a small offroad rated lamp connected to a 3-cell lipo battery (3 cell lipo's deliver around 12.5v fully charged). These batteries are rechargeable and also small and lightweight for the voltage and mAh ratings. You can find them at any hobby store
The light is EXTREMELY bright for a handheld, and whereas I already use these lipo packs for other hobbies, I have plenty of them lying around. It generates a good amount of heat, but I only use it intermittently as a spot or search light.
You could do something very similar. Buy a cheap car headlight or better yet, a driving light that comes in a housing. Cobble a handlebar mount for your bicycle. Wire a switch between the lipo battery and the lamp, and presto... super bright bike light.