I didn't know much about Bailly before he came to United, but I'd wager there's a good chance Mourinho's coaching has actually improved Bailly up a tier or two from his level at Valencia, or at the least he's helping him to find consistency in his game. Again I have no idea how highly rated he was before, but at the time we signed him, it was very much a surprise signing for most United fans (and other fans). Perhaps the demands of the PL align better for Bailly than La Liga did.
Yeah I'm sure there's a massive psychological component to it, that has helped Bailly to gain confidence and raise his natural talents to another level. I remember an older interview where Ibra commented that Mourinho, during their Inter days, gave Ibar a ridiculous amount of confidence where he felt like Superman, and could do anything.