Although not precisely a bicycle enthusiast and certainly not an expert rider, I must admit that it must be a thrill moving around Barcelona on a bike. The more bicycle friendly the city gets the more frequent it is to find groups of riders exploring not only the small alleys of the old part of town but also big arteries like Passeig de Gracia (picture).
There are several companies providing this guided tour services in Barcelona. You can easily see the name of the agency on the guide's T-shirt (Barcelona Ciclo Tours), but of course you have a great selection where to choose from. Here is a good list of bike rentals in Barcelona.