Adam Bowman was born in Forfar, Scotland. He played centre-forward for St Johnstone and East Stirlingshire in the Scottish League before joining Everton before the beginning of the 1902-03 season. That year Everton challenged for the title and Bowman was only selected to play in nine games.
Blackburn Rovers looked like they would be relegated that season. Joseph Walmsley, Blackburn's manager, desperately needed someone to score goals and in March, 1903, persuaded Bowman to join the club.
On Easter Monday, Blackburn Rovers had to visit Bowman's former club. Blackburn surprisingly beat Everton 3-0 with Bowman scoring two of the goals. Four days later, Bowman scored another two goals in a 3-1 victory over Newcastle United. These two results meant that Grimsby Town, rather than Blackburn was relegated from the First Division of the Football League.
Rumours began to circulate that Blackburn Rovers had bribed Everton players to lose the game. Officials at Grimsby lodged an official protest and the Football Association decided to hold an inquiry into the game. A report by the FA claimed that there was evidence that Joseph Walmsley had tried to arrange a win for Blackburn Rovers. However, they believed that Everton players had not taking any bribes and that the final league placings should remain unaltered. Walmsley was immediately banned from having any further involvement with football.
In July 1903, Robert Middleton, a former school teacher, was appointed as Blackburn's new secretary/manager. Middleton purchased Bob Evans, a Welsh international goalkeeper, from Wrexham for £150. In November, 1903, Middleton also persuaded Fred Pentland, a regular goalscorer for Blackpool, to join the club. Pentland scored seven goals in 18 league appearances, but his efforts could not stop Blackburn from being involved in another relegation struggle. The club eventually finished in 15th place in the league. Lionel Watson was the club's top scorer with 14 goals.
It was the same story the following season. Despite good individual performances from Adam Bowman, Bob Crompton, Bob Evans, Fred Blackburn, Arnie Whittaker and Fred Pentland, Blackburn could only finish in 13th place. Bowman was the top scorer with 13 goals. In an article that appeared in the Blackburn Times a journalist wrote: "Like its two predecessors, the season of 1904-05 has been one of disgrace to the Rovers".
In April 1905, Robert Middleton signed Welsh international striker, Billy Davies from Wrexham. At the same time, two of Blackburn's best players, Lionel Watson and Fred Blackburn, joined West Ham United. Blackburn, an English international, left because he was upset with the decision not to grant him a benefit.
Bowman only played a few more games before moving to Brentford in the Southern League. During his time at Blackburn he had scored 43 goals in 99 games. In the 1908-09 season Bowman scored six goals in fifteen games for Leeds City. He also played for Portsmouth and Accrington Stanley before retiring from the game.