Hull boss Bruce, a former United captain under Ferguson and once considered a potential successor, has huge respect for the way Moyes has taken on one of the thorniest tasks in the game.
Replacing Ferguson, whose trophy haul and longevity at Old Trafford are unprecendented, has been described as an impossible task and, with the champions eighth in the table after winning just eight of their 17 games, Moyes has hardly enjoyed a straightforward start.
But Bruce, whose side host the Red Devils on Boxing Day, appreciates better than most the pressures of life at Old Trafford and believes the Scot will be a success given time.
"I think whoever had taken over would have needed a bit of time," he said.
"Sir Alex must be there in every closet, behind every door you open. Thankfully they have shown what kind of a club they are, giving David a six-year deal. They will give him time and rightly so. The change has happened and I think we're all getting used to seeing David standing there now.
"It's never easy to follow someone like Sir Alex, with the record he's got. But he's an outstanding manager, David, and it's just a matter of time before things click into place.
"He'll have to have his own stamp on it, like anyone in management, but he's proved over the years what a good manager he is. He's a football man and all of us in the game, us British ones at least, are delighted that the big, top job has gone to somebody like him because he deserves it."
Whether or not Bruce can put a fresh spanner in the works for Moyes, who has overseen four consecutive wins in all competitions since losing successive matches against Everton and Newcastle, could depend on his defenders.
The Tigers have conceded the fewest goals in the league on home turf - just three in eight matches - an unlikely statistic for a promoted side and also a point of some pride for former centre-half Bruce.
He accepts his back-line, led impressively by skipper Curtis Davies and directed by Scotland goalkeeper Allan McGregor, must be at their best once more to keep United quiet but they have previous this season - with the prolific Luis Suarez quiet during Liverpool's 3-1 defeat in East Yorkshire earlier this month.
"We've been good defensively and we'll need to be good again because with Manchester United coming to town they can score from all sorts of areas," he said.
"Rooney, Welbeck, Hernandez, Valencia, Cleverley, Jones, Smalling...take your pick because the list is endless. They've got big players who want to win, want to entertain and want to beat you: that's not going to change.
"They have found a bit of form, as you would expect, and they were convincing winners (3-1 over West Ham) at the weekend. So it's one where there is no real expectation on us, it's all on them.
"We have to make sure we play well. We did that against Liverpool and caught them on an off day. We have to enjoy the occasion and enjoy the challenge of facing Manchester United.
"So let's not have too much turkey at Christmas and put up a really good display."