The Tigers have yet to play at home in the competition but have secured a fifth-round clash at the Amex by seeing off Middlesbrough and Southend.
A third win against lower-tier opposition would put them into the last eight and open up the tantalising prospect of a trip to Wembley.
Bruce has been low key about the cup thus far, making significant changes to his starting XI and declining to speculate about his team's chances of replicating Wigan's surprise win last season, but that is beginning to change.
"I think once you get to this stage of the cup it's different," he said.
"If we can get past Brighton then all of a sudden you're in the quarter-finals and it starts getting exciting, certainly if you can get a nice draw.
"With four of the biggest teams - Chelsea and Manchester City and Liverpool and Arsenal - drawing each other there's an opportunity for someone somewhere along the line. Why not us?
"If we get through and are drawn against anyone at home apart from the big four, it starts to get tasty.
"One thing we can't do is win the Premier League but as we saw with Swansea in the League Cup and Wigan in the FA Cup, anything is possible in those competitions.
"You win five games and you've won the cup. So let's get past Brighton and have a good run, why not?"
One player who will have no say in Hull's cup ambitions is defender Paul McShane.
The Republic of Ireland international is to undergo ankle surgery on Monday, with his season almost certainly over.
McShane was injured in a collision with Tigers goalkeeper Steve Harper during Tuesday night's defeat by Southampton.
Although scans revealed no break, there is serious ligament damage and manager Steve Bruce believes McShane is unlikely to be seen again until next term.
"We knew it was a serious one when we saw the pictures, his ankle was practically the other way around, so Paul has an operation on Monday," said Bruce.
"It's not broken but he's severed a couple of ligaments in there that need repaired.
"We don't know the real extent until the surgeon goes in but I wouldn't have thought he'll play any more part in this season.
"I would have thought it will be about six months out, so maybe the best case scenario is to be fit for the start of next season."
Hull's defensive resources are stretched somewhat at the moment, with McShane joining James Chester and Liam Rosenior on the sidelines.
Chester and Rosenior are making good progress in their own rehabilitation and could be in contention for Hull's next Barclays Premier League clash at Cardiff.