The 30-year-old, who played alongside Phillips between 2018 and 2022, praised the midfielder for his attitude.
Speaking on BBC Radio 5 Live's new My Mate's A Footballer podcast, he said: "Kalvin Phillips is one of the nicest kids. He is always smiling and is just a proper nice guy.
"He deserved it [his move to Manchester City]. When he was playing for us at Leeds, he was obviously integral to how we played and England too. When he first went into England he was playing slightly higher up which surprised some of us as Leeds, but he did well.
"It's tough for him, because he's going from probably being one of the best players at Leeds to Man City where the best players in his position [with Rodri] is just like a metronome. There's not even much you can say to him. When he comes into the team, they're always going to draw comparisons between them."
Phillips has been called-up to the England squad despite struggling for regular game time this season and Bamford knows he will not be happy with his current situation.
"He's obviously going to look at what he can do to get back playing - and whatever that means for him," Bamford added.
"This is one of those where the public say he should just be happy because he's getting paid an absolute fortune, but there is no way, no matter how much you're getting paid, you cannot be happy sitting on the bench.
"I think it is one where he is chasing to get back in the England team and any footballer is going to choose playing over getting that extra bit of money."
Warning: some strong language