Bruce oversaw a major surprise on Sunday when the Tigers defeated Liverpool 3-1 at the KC Stadium, but a second shock win over the Barclays Premier League leaders would be an even bigger shock.
He understands why that is the case - pointing out that he is hoping for survival while Gunners boss Arsene Wenger targets the title - but believes anything is possible.
"We knew from the start of season we'd be underdogs. We were favourites in many people's eyes to go down and that's normal for a team coming up from the Championship," he said.
"But we've been very consistent and played to a level that has given us a chance. We can't have many off days and we certainly can't have one on Wednesday.
"We've got to be at full tilt to win a game in the Premier League but, then again, I think there are 12 or 13 teams like that.
"The beauty of Premier League is nobody can predict it. We see the big teams in Spain or Germany just blow away the rest of the league, that's not the case here so far.
"Everybody has had a bit of a struggle and that shows the strength in depth of the league and that's why it is watched all over the world."
Bruce, meanwhile, has praised son Alex for the way he has coped with his unique circumstances and forced his way into the side.
Bruce senior did not initially intend to bring the central defender with him to the KC Stadium, but the combination of Hull's shortage at the back and the collapse of a move to Major League Soccer saw him sign on a free transfer in July 2011.
He went on to play 37 times for the Tigers in 2012/13 as the side won promotion to the Barclays Premier League but there has been no hint of favouritism from his father.
Summer signing Curtis Davies, James Chester, Abdoulaye Faye and Paul McShane have all been preferered to Alex Bruce this term but he put in an impressive shift on his Premier League bow against Tottenham and returned to the side for Sunday's surprise defeat of Liverpool.
He is set to keep his spot at the Emirates.
"Alex has handled the situation very well. He's mature enough," said the manager.
"He's had to put up with that all his life. He's had to deal with it since he was 11...people said he was only in the school team because of who his dad is.
"It's always a difficulty and he's had to fight with it for all his young career.
"But I brought him in last year because I knew he could play in the Championship. He'd played two years for Leeds and four years for Ipswich. He's played in the division week in, week out there so I had no problem in that respect.
"The big goal is to play in the Premier League but he understood that the team played particularly well at the start of the season and he had to wait for his chance.
"But we've had a couple of injuries and he took his chance on Sunday. I have to reward him, like I have to reward everyone else."