Good, cheap, powerful. Pick any two.....
The simple answer is you can't do "cheap" and still be much good. If cheap comes in front of "good" then i'd be looking for some 24v truck fan motors, which can run over 500w, and use a cheap ebay motor controller to drive it, with a couple of 12v small lead acid batteries in series for the energy storage.
Any HV AC motor is going to be a pain to drive, and not to mention a significant safety risk on a bike (which gets wet, gets dropped, generally isn't very well looked after etc)