This question is asked with surprising regularity, eg:http://www.endless-sphere.com/forums/viewtopic.php?f=28&t=29978
Along with questions about perpetual motion (I am not being rude or sarcastic, I am serious, that is a surprisingly often raised topic).
The almost uniform answer is that you would be better off using the ice engine to directly power the bike rather than a generator. Apart from the physics of the whole thing, one of the main advantages of an electric bike is that a) it makes almost no noise, b) uses no fossil fuels (directly) and c) is stealthy. If you are going to ruin a) b) and c) with an ICE engine, why not just build an ICE bike (which if you are not getting the benefits of a) b) or c) are a superior form of power to electric.