He showed so much promise that, in 1751, the Secretary of State, José de Carvajal y Lancaster, personally provided him with the funds to go to Rome and study under the direction of Corrado Giaquinto.
He immediately joined the Royal Tapestry Factory; painting the designs and "cartones" (cartoons), under the stylistic direction of Anton Raphael Mengs.
He originally copied works by other artists, such as Luca Giordano and his mentor, Giaquinto, but later created his own, based on scenes from daily life.
He also did some book illustrations: notably drawings for the 1780 edition of Don Quixote, which were engraved by Manuel Salvador Carmona and Fernando Selma.
Shortly after Bayeu's death (and not long before his own), he tried again, with recommendations from several artists, but was still unsuccessful and the post was left vacant.