Bruce's side are fourth in the table going into Monday night's game at Burnley but just a point separates them from second-placed Watford and they are only behind Crystal Palace on goal difference.
They were beaten 4-2 at Selhurst Park on Tuesday though and slumped to a 4-1 defeat at Bolton in their previous away game to raise concerns at their ability to go the distance.
But Bruce is confident they can stay in contention for promotion, as long as they do not let nerves get the better of them.
"We're delighted we're there because no one gave us a cat in hell's chance at the start of the season," he said.
"There's 10 (games) to go and there's still lots of twists and turns for us and every other side that's up there going for promotion.
"After Easter weekend, once we've played Watford, that's when the tickly bit really starts but the message is always to enjoy it.
"It's important not to get over-cautious. You've got to try and enjoy the experience rather than getting bogged down by it.
"All we can do is give our best crack. If we give it everything we've got, and I'm sure we will do, then that'll do me. I know we won't be far away."