Bailly has been a key player in United's strong start to the new season, but the defender was dropped for the win over Crystal Palace due to what Mourinho said was "fatigue".
The centre-back has formed a solid partnership with Phil Jones, with the duo helping Mourinho's side conceded just two league goals in the campaign so far.
However, Chris Smalling and Victor Lindelof will be waiting for their opportunities on the sidelines and Marcos Rojo will be hoping to impress when he returns from injury, meaning Bailly is not taking his position for granted.
When asked if competition was good for the players in the back line, Bailly told 'United Review': "It's very important for us, it's important for the team, it's important for the manager, and when it's like that, there is also competition amongst ourselves, so we always have to improve because I don't think anyone is automatically entitled to their position in that team.
Bailly added: "There's a good relationship between Phil and me, and with the other two defenders, Victor Lindelof and Chris Smalling, even though we've not had the chance to play together yet.
"It's fine in my view because there are four of us defenders and everyone is ready to make the most of the opportunities the manager gives us. To defend as well as possible and concede less goals, that's the aim for all of us."
The defender also heaped praise on Mourinho, the man who brought him to Old Trafford as a 22-year-old, saying his influence has helped him improve drastically.
"For me, the aspect that was very important and where I see improvements - and can improve even more, to be honest - is the tactics, as well as the high level of concentration that's required," said Bailly.
"For a young defender it's very important and with this manager I'm positive about the future."