Bowman started his senior career with Hearts, making 116 league appearances before leaving in 1984. He moved to Coventry City for two seasons where he was joined by Jim McInally, signing from Nottingham Forest. They left together in 1986, joining Dundee United for a combined £140,000 transfer fee and reached the 1987 UEFA Cup Final in their first season therebeating Barcelona home and away in the quarter-finals and then eliminating Borussia Mönchengladbach in the semi-finals. They lost 2–1 on aggregate in the final against IFK Göteborg.