Born in Maesteg, Bowen first played for Northampton Town. He had only played 12 times for Northampton before catching the eye of Pat Whittaker, son of Arsenal manager Tom Whittaker. He was duly signed by Arsenal in the summer of 1950 as an understudy to Joe Mercer at wing half. He made his debut against Wolves on 24 March 1951, he only made a handful of appearances between 1951 and 1954. Arsenal won the old First Division in 1952-53 but he only made two league appearances all season. In 1954-55, after Mercer had retired due to injury, Bowen became a regular in the Arsenal side, and would continue to be for the rest of the decade.

Bowen had also made his debut for Wales, in a friendly against Yugoslavia in September 1954. Bowen went on to win 19 caps for Wales, and was the team's captain for their 1958 FIFA (Fédération Internationale de Football Association) World Cup campaign. Wales drew all three of their group matches and qualified for the quarter-finals, where they were beaten 1–0 by Brazil, the goalscorer being a 17-year-old Pelé. Along with goalkeeper Jack Kelsey, Bowen was the first Arsenal player to play in a World Cup.

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