Bruce's men ensured a place in the last eight on Monday with a 2-1 win over Championship side Brighton and Hove Albion - Curtis Davies and Robert Koren putting Hull ahead before Leonardo Ulloa pulled one back in the second half for the visitors.
Hull have not played in the FA Cup semi-finals since 1930, but now face League Cup finalists Sunderland in the quarter-finals for the honour of a trip to Wembley in the last four.
And Bruce believes his side, who moved six points clear of the Premier League relegation zone with a 4-0 win at Cardiff City last Saturday, can afford to dream about potential cup success.
"The last time was 1930 (when Hull reached a semi-final), wasn't it? There's not many around who went to that one," Bruce said.
"We've given ourselves a wonderful chance. It's a nice position to be in and now we've got to see if we can make it a really memorable season.
"(Wembley) is a wonderful occasion and, when you sit back in your cardigan and slippers, you remember the FA Cup. I've been fortunate enough to win it (as a player with Manchester United) and it would be nice to go back there again if we possibly could.
"It's all to play for. We've got to beat Sunderland yet but (Wembley) is a wonderful day out - the best day you'll have as a player or a coach. But more importantly it's for the supporters - if they can get that it's terrific."
Ulloa's goal made life nervous for the Yorkshire club in the latter stages of Monday's game, and Bruce was not surprised by the spirit of the second-tier side.
"In the first half we were completely in control of it. We just needed a third and the game was over," he added.
"It was almost job done, but how often do we see that? Just at the right time Brighton got the goal and fair play to them.
"All of a sudden it was a cup tie again."
