expatriate, I think you'll find a number of threads about bicycle ownership in Madrid on this message board - just conduct a search. But it's really not recommended because it can be quite dangerous competiting with cars, the saturation of sidewalks with pedestrians, high rate of bicycle theft when they're parked/chained outside, etcetera.
Maybe people on Spain's
www.SegundaMano.es sells used bicycles. Give them a try.
Best of luck! Saludos, MadridMan
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