Here there is a "taller" to repair your bike and take parts of bikes that are not in use. If you know how I think you can build your bike there (maybe some part you must to buy in a bike shop, but you can try, they have a lot of old bikes). The page is:
It's open on saturdays.
Horario del Taller de Bicis:
Sábados 18:00h a 21:00h.
c/Joaquim Valls 137, 9 Barris, Barcelona