Bromage graduated from the Port Vale youth team to sign professional forms in October 1977, with the club in the Third Division and under the management of Bobby Smith. He made eight appearances in 1977–78 as the club were relegated into the Fourth Division. He then scored on the first day of the 1978–79 season in a 2–2 draw with Scunthorpe United, and then found the net again in a 3–1 win at Doncaster Rovers on 12 September. He finished 1978–79 with two goals in twenty games. Bromage made thirty appearances in 1979–80, and after being a fringe player under Dennis Butler and Alan Bloor he established himself in the first team under John McGrath. He again scored past Doncaster Rovers, adding the third of a 3–0 win at Vale Park in the last match of the season. He went on to score five goals in 52 appearances in 1980–81, finding the net in a League Cup clash with Tranmere Rovers, before bagging a brace in the league against Tranmere, and adding to his tally with strikes against Bradford City and Hartlepool United. Moved from midfield to left full-back, his performances there he was voted Player of the Year by the club's supporters. He made another 54 appearances in 1981–82, before he helped the "Valiants" to promotion in 1982–83 with 2 goals in 49 games. He was selected in the PFA Team of the Year for 1982–83, along with teammates Phil Sproson, Geoff Hunter, and Steve Fox. He served as club captain and was rated as an excellent captain by teammate Robbie Earle. However he refused to sign a new contract for the 1983–84 season, as did teammates Geoff Hunter, Barry Siddall, and Terry Armstrong. He eventually walked out on the club, and played two Second Division games for Oldham Athletic in October. However he returned to Vale Park in November, and agreed to sign a new contract. He went on to finish the campaign with 42 appearances, scoring one goal against Wigan Athletic, as the club were relegated under new manager John Rudge. Bromage posted 46 appearances in 1984–85, finding the net in a league win over Stockport County and an FA Cup victory over Scunthorpe United. His consistency won him a place on the PFA Team of the Year for a second time. He won his second promotion with the club in 1985–86, posting 51 appearances and scoring one goal, again against Scunthorpe. The 1986–87 campaign would be his last with the club, and he played 51 games, scoring one goal in a defeat at Walsall. He played a total of 402 games for the club in all competitions, scoring 15 goals. He was sold to Terry Cooper's Bristol City for £25,000 in August 1987. His Port Vale testimonial match was held against rivalsStoke on 13 April 1986, Vale lost the game 1–0. City reached the Third Division play-offs in 1987–88, however lost out to Walsall in the final. An eleventh-place finish followed in 1988–89, before promotion was finally won under Joe Jordan in 1989–90, as City finished in second place, two points behind rivals Bristol Rovers. In all he played 46 league games for the club, scoring one goal. Bromage joined Barry Lloyd's Second Division Brighton & Hove Albion for the 1990–91 season, but played only one game in their run to the play-off final. He instead joined Fourth Division Maidstone United on loan, playing three games. He later served Southwick as a player-coach and Littlehampton Town as player-manager.
