Bruce applied to succeed Mick McCarthy in February, but Terry Connor was preferred and Wolves were subsequently relegated from the Premier League.
The Tigers have now won five of their last six matches, but Bruce played down the significance of their latest victory.
He said: "It's football. At one time thought I was close, but it's gone, it's history, I'm just pleased we've got the result."
Excellent goals from Sone Aluko and Jay Simpson fired Hull into a commanding lead, although James Chester's own goal set up a tense finish.
"We were so comfortable and made two mistakes really, one from the goalkeeper, and a miskick from Paul McShane. It made it a bit more nervy than it needed to be," Bruce added.
"Overall, with the quality of the two goals we scored, we probably deserved it."
Hull are now fourth in the table, but Bruce continued to play down talk of a return to the top flight.
"We're what, 15 games in? It's important we stay injury free. It's key over the winter months who can stay fit. That's when you need your squad," he said.