Power drills really aren't made for sustained use and car batteries are heavy. You would probably burn up the motor & bushings fairly quickly. Try one of
these.
You will need to get a charger and Lithium Ion batteries. Don't bother with the NiMH. They will not provide enough power.
I have one of these chainsaws and it works amazingly well. Since it drives a chain, it should be fairly easy to rig up to a bike.