Solskjaer eased the pressure on his job at Old Trafford with an 11-game unbeaten run before the coronavirus pandemic led to the shutdown of football across Europe.
The Norwegian has made a point of investing in young players, as well as promoting academy graduates, during his time as United boss and Bailly has said the club's former striker has the right management style off the pitch to nurture an inexperienced squad.
"He's someone that will always talk to you," Bailly told ESPN.
"He always communicates well. He gives you so much confidence because as a footballer, you go through moments where you feel low and he can read that and when he sees that he immediately comes over to you and talks to you.
"He offers advice so that you can regain confidence and for me, that's so important because we have a very young team and if we have a coach or manager like that then the team will go from strength to strength."
Bailly has struggled with injury during Solskjaer's time in charge but he still impressed enough for the club to trigger a two-year extension to his contract in January.
His deal runs until June 2022 and the centre-back, fit again after more than six months on the sidelines with a knee ligament injury, is happy that his immediate future will be spent in Manchester -- even if there is a downside.
"When I'm asked about Manchester, as a joke I always say the [best thing] is the weather because we all know the weather isn't good!" laughs Bailly.
"But what I really like is the atmosphere, the moments that I get to live out with the club. Here, people really live for football. Their passion for the game is enormous so for me, being here, I realise that we need to always give our best.
"To just sign to play for Man United is a dream. To be a part of a team this big is the best thing.
"That's why I'm so proud to play for Man United and that's why I give everything I can when I'm out on the pitch. I will literally give all my strength to this club."
Bailly, 25, has been in fine form since returning to the team. In the four games he has started since returning from the injury he suffered in a friendly against Tottenham in July, United have a perfect record, scoring 15 goals without conceding.
The Ivory Coast international went almost 10 months without starting a Premier League game before making his comeback in the 2-0 win over Chelsea at Stamford Bridge in February and he said it was a stern examination after so long on the treatment table.
"If you've not been playing for a long time, in a league as strong as this one, the truth is that it's hard," he said.
"Imagine with an injury as long as mine too! But the truth is, I've been lucky with my teammates to have their help and support and I had a phenomenal return.
"It was a difficult match against Chelsea, my first match back, and thank god that we won."
Bailly is playing catch up after missing so much of the season and has work to do to dislodge Lindelof but, for now, he is just happy to be out of bed.
"I'm lucky to have my family -- my mum, my dad, my kids, my missus and my friends," Bailly said. "I can't say it was easy but, having them around helped to not make my recovery as difficult.
"At the start it was difficult because I couldn't even go to the gym to work out, I basically had to stay in bed. But towards the end, I got to come back here to Manchester and I got to go to training and the gym again and to the physio and I finally felt like an actual footballer again.
"The fans are so important. They're the 12th man, you know?
"I want to say thank you because during my injury, I got a lot of messages of support so thank you. And now, in return, I have to give my best so that they can enjoy the game as well."