No, you have no right to a refund for anything you purchase from a shop unless it is faulty and "not fit for purpose". If the bike is working as it should but you just don't like it, then the shop MAY decide, as a good will gesture, to give you a refund.
The only time you have the right to return something for a refund is when you buy something over the internet or from a catalogue where the distance selling act comes in to play