The club's top scorer had a hernia operation after netting the winner against West Ham at the end of last month.
At the time there were fears he could be out for over a month, but Bruce said: "Robbie has trained this week which just goes to show what the medical people can do. It's just over two weeks since the operation.
"We'll see for a reaction but as long as there isn't one he'll come straight back in the squad. It's quite remarkable what they can do to fix what is labelled as a hernia.
"To be playing in two and a half weeks shows what they can do. He's pain free and running around like a two-year-old so let's hope he stays like that."
Having been buoyed by Brady's recovery, Bruce is also hoping to have good news over his quest to tie down Sone Aluko - whose initial two-year contract expires next summer - to a new deal.
"I'm going in to have a word with my bosses to see if there's any development," said Bruce. "Maybe we'll know a little bit in the next few days.
"We're trying out utmost to get it over the line so let's hope this time next week everything will be hunky dory. At the moment we're still boxing a bit."