Born in Barcelona, Catalonia, Busquets was a FC Barcelona graduate who joined from neighbouring CD Ciutat Badia and possessed very good technical skills for a player in his position, and he made his La Liga debut for the first team on 7 November 1993 in a 2–1 home win over Racing de Santander, going on to appear in the following two games. However, he was mostly back-up for Spanish international Andoni Zubizarreta during his first years; he did manage to feature in the 1990–91 European Cup Winners' Cup final in a 1–2 loss against Manchester United, with two goals from Mark Hughes.