Hull take on Bruce's former club Sheffield United in Sunday's semi-final, with the winners taking on either Arsenal or holders Wigan Athletic - another of his former employers - in the final next month.
The Premier League club are aiming to reach the final for the first time and Bruce, who lifted the famous trophy three times in his playing days at Manchester United, has his sights set on winning the FA Cup for the first time as a manager.
"It is not often you get to an FA Cup final as a player or a manager," he told the Daily Mirror.
"I was fortunate enough to win it three times as a player, but it's taken me 16 years to get to a semi-final as a manager."
"If I could win as a manager, it would be up there with the best achievements of my career."
League One outfit Sheffield United side and Championship club Wigan have claimed some notable scalps to secure their places in the last four.
And Bruce is pleased to see some surprise packages in the latter stages this year, claiming it has re-energised the competition.
"I think it is so refreshing to see the FA Cup not being dominated by the big boys. It's brought a bit of sparkle back to it," he added.
"Sheffield United versus Hull City in the semi-final – I don't think many people would have picked that at the start of the season.
"And how well have Wigan done again after beating Manchester City to lift the trophy last season?"