The Magpies take on Ole Gunnar Solskjær's side on Thursday (kick-off 5.30pm GMT) aiming to build on Saturday's 1-0 triumph against Crystal Palace, elevating Bruce's side into ninth place in the top-flight.
Bruce - a three-time Premier League winner with Manchester United - expects a difficult encounter against the Red Devils, who suffered a 2-0 defeat away at Watford, currently bottom of the table.
Bruce said: "Manchester United weren't at their best but Watford were excellent and they were bottom of the league with nine points up until yesterday. They'll be disappointed after what happened yesterday and that's always a danger sign.
"A bad result and they always come out and want to try and erase that. It's in their DNA. Make no mistake – when you go to Old Trafford, you're going to have to play well, be brave when you have the ball and pose them a threat.
"We'll enjoy the challenge of taking them on and we managed to beat them a few weeks ago so let's see if we can do that at Old Trafford.
"They've got good players so we'll have to be at our best to try and get something but we're quietly confident.
"It's going along okay at the moment but we've got Man United, Everton and Leicester - a hard, hard week lies upon us and that's the beauty of the Premier League and how tough it is.
“We’ve given ourselves a nice platform, but we’re only halfway there. We’ve got to show the same resilience we’ve shown over the last few months, and see where it takes us.”
Newcastle's narrow win over Palace also saw Miguel Almirón break his goalscoring duck as the 25-year-old's late winner ended his unwanted run of 27 games without finding the net.
Along with the Paraguayan, Bruce was full of praise for his squad after Saturday's narrow win over the Eagles sealed a third league win in their previous four games.
Bruce added: "I was just delighted for the lad himself and I think everybody else who supports Newcastle and has watched the team for the past 12 months. I saw a stat that it was his 47th shot on target so it's great for him.
"As I've said many times, he's a great pro and a great lad and he lights up the place every day when he works. When someone is like that, you want them to succeed and do well and let's hope it is the start of a few.
"I can't fault their attitude and their spirit for it because at the end of the day, we set them up and they've got to show they are resolute and difficult to play against and difficult to beat.
"The way they are speaks volumes. They're a good group and if they stay like that, they deserve the rewards they are getting at the moment. For the way they are and the spirit they've show, I've got to very pleased over the last few months."
