The newly promoted side have slipped to defeats against title-chasing pair Chelsea and Manchester City in their opening three games, but battled to a 1-0 win over Norwich City despite playing most of the game with 10 men.
Second-half goals from Alvaro Negredo and Yaya Toure consigned them to defeat at the Etihad Stadium on Saturday, but Bruce is enthused by their performances thus far.
| HULL CITY TIGERS LATEST
|8/13||Hull are 8/13 with bet365 to be relegated this season
"We need now a little bit of luck in terms of the window shutting and obviously staying injury free and suspension free. We haven't got the biggest of squads. But if we sat injury free then we’ve got an outstanding chance.
"You bring in the likes of Tom Huddlestone and Jake Livermore and suddenly the quality of your team rises. We’re delighted we’ve got them. A lot's been said about footballers for all the wrong reasons but those have just wanted to go and play."
Winger Robbie Brady is the only Hull player to have scored this season and Bruce admitted he is still looking to bolster his attacking ranks, despite the signings of Yannick Sagbo and Danny Graham.
Sagbo is currently serving a suspension for violent conduct, while Sunderland loanee Graham has not found the net since January 9, when he was a Swansea City player.
He added: "It would be easy to say 'yeah, we need a striker', but the ones that are going to make the difference for us, 'will they come?' Because the ones that will make a difference will have competition and no disrespect to us as a club but that’s difficult.
"Also can we afford them? And who's out there? Who's going to get you 12 or 15 goals to make you okay?
"So it's very, very difficult but we’ll keep working away at it and see what we can do and see what we can come up with in the next 48 hours and put an end to this madness that has been this window."
Bruce did not rule out Nicklas Bendtner coming to the KC Stadium.
The 52-year-old added: "I've had him twice before and he did very, very well for me at Birmingham and Sunderland but again can we get him to come to us? And can we afford him?
"It’s difficult for us, he’s playing for Arsenal and we’ve just come out of the Championship, but we’ll see."