The Tigers have only reached the semi-final stage once, back in 1930 when they lost to eventual winners Arsenal after a replay.
However they will make the last four of the competition for the second time if they can beat Bruce's former club Sunderland at the KC Stadium on Sunday.
Hull have already defeated the Black Cats 1-0 at home in the Premier League this season in November as well as claiming a 2-0 victory at the Stadium of Light last month.
Bruce, who captained Manchester United to FA Cup glory in 1994, said: "When you put it into context, if we win it then we have never been in the semi-final since 1930 so I don't know if there are many supporters around who went to that last semi-final - I hope there is - and that puts it into context of exactly what it would mean to everybody.
"Of course, the Premier League, we all want to play in it and be part of it, but there is nothing quite like the FA Cup too.
"If you can get to the semi-final stage then believe me it's something that you look back on your career and think of as a good or a really special occasion, and if you have the fortune to win it then it stays with you a long, long time.
"We have got a wonderful chance but then again there are eight teams left in it and everybody's got a chance and as we have seen last year in the competition, my old club Wigan won the thing which I think everybody got a delight.
"The League Cup before that Swansea won it so there is a competition that the so-called smaller teams can win.
"On a one-off you have to win five or six games and you can win a trophy. We have won three so we have got to obviously win the next big couple of games coming up and if we can beat Sunderland it will be a great occasion for everybody."
Defender James Chester has revealed that Bruce has been delivering the Wembley message to his squad in training.
"To get the opportunity of going to Wembley is something special, the gaffer's been telling us it won't come around too often in our careers so I'm looking forward to trying to achieve it," he said.
"The main goal this season was to stay up and we're on the way to achieving that, but the cup run has been a nice distraction.
"To create history for the club would be nice for the players. Getting two victories over Sunderland in the league means we're full of confidence."