In 1984, Bute, then known as Johnny Dumfries, was the sensation of the F3 season, scoring 14 race victories on his way to winning, and completely dominating, the British Formula 3 Championship for Team BP (Dave Price Racing). He also finished runner-up to Ivan Capelli in the European Formula Three Championship that year. In 1985, he graduated to the newly created FIA International Formula 3000 Championship, initially competing for Onyx Race Engineering before switching to Lola Motorsport. It was a disappointing season, with a sixth-place finish in Vallelunga being the highlight of the year.