Jose Mourinho's men opened their campaign in emphatic fashion, thumping West Ham 4-0 at Old Trafford on Sunday (13 August) and travel to Swansea for this weekend's early kick off hoping to make it two wins from as many games.
While the season is still in its very early stages, United's performance in their opening game prompted some to suggest they will be among the title contenders come May.
"The team has always been at a world class level, they have just had some bad moments," Bailly told the Guardian in a wide-ranging interview.
"But now it's time to give Manchester United its value. That comes with our hard work and that's what all the players do that come - like [Romelu] Lukaku and Paul [Pogba], and also [Victor] Lindelof. With all the hard work we put in we are going to demonstrate that we are again a world class club."
The Ivory Coast centre-back was a surprise signing when he arrived from Spanish side Villarreal for £30m last summer, but went on to establish himself as one the first names on Mourinho's team-sheet.
Despite a knee injury in October that ruled him out for six weeks, the 23-year-old played 38 games in all competitions in his first season in English football, lifting the League Cup and playing a major role in United's Europa League triumph, even though he missed the final through suspension.
Yet, despite a successful first season, Bailly admitted he was slightly taken aback by the challenge of joining the 20-time champions of England.
"When I came to Manchester, it was a bigger step from when I was in Villarreal," he said.
"It is something that is not easy, when you come to a team where there are players that have more experience in the English league.
"I had to see how the football was played. For me it wasn't difficult because I had very good team-mates that helped and were always looking after me, all of this helped me join the group and that is why it wasn't that difficult.
United have since added three more signings to their squad, spending £75m on Lukaku, £40m on Nemanja Matic and £30.7m on Lindelof. While the latter did not even make the squad on Sunday, he is expected to provide competition to Bailly and the duo are widely expected to become United's first choice centre-backs, largely due to Phil Jones and Chris Smalling's poor injury record.
Since Sir Alex Ferguson's departure at the end of the 2012-13 season, United have struggled to field a settled back-four but there is a growing feeling things might be about to change under Mourinho.
Throughout his career, the Portuguese has built his sides on a solid defensive unit, such as John Terry and Ricardo Carvalho at Chelsea and Marco Materazzi and Walter Samuel at Inter Milan.
Bailly's no-nonsense style has drawn comparison with that of two of the greatest defenders to ever play for United, Nemanja Vidic and Jaap Stam, and the former Villarreal man believes Mourinho is the right manager to help him develop even further.
"I've had the luck to have a manager in Jose Mourinho from whom I can learn more and I must work hard and listen to what he says," explained the Ivorian.
"To achieve success, you have to take the example of players like Vidic and Rio Ferdinand.
"I have to try to follow in their footsteps. It's very difficult, but everything is achieved with hard work, keeping my head high to keep moving forward."