QPR had the chance to claim a point late on, but Charlie Austin's penalty was saved by Allan McGregor.
"Well we knew it was never going to be easy. A newly-promoted club, a few new signings, all the hype of their first game of the season, and we've come away and we've won one which is always a great start," Bruce told Sky Sports News.
"It took us a while to get going, I have to be honest, but second half in particular we just about edged it."
Hull continue their Europa League campaign on Thursday when they play Lokeren in Belgium.