The Whites landed their first signing of the summer transfer window earlier this week in the form of the Blues youngster.
United announced the capture of the 18-year-old wide man on a four-year deal from St Andrew's for an undisclosed fee.
Miller made five Championship appearances under Bowyer last term after his side had secured their league status at the end of the campaign.
The winger signed an initial two-year scholarship but turned down professional terms at the club he has been with since he was 10 years old to make the move to West Yorkshire.
He will initially link up with Mark Jackson's Under-23s side in the Premier League 2 with a view to stepping up into the first team ranks in the coming seasons.
“Is it a blow? You are talking about a young kid that just came on in the last six or seven games of the season," Bowyer told Birmingham Live over Miller's decision to leave his squad.
“I introduced him because I like him. Is he ready to go and start Championship games tomorrow? I don’t believe so.
“But we would have developed and he would have improved with us and he would have got more game-time with us.
“But that’s his decision, you know. He is a young lad, he has gone to a good club, I don’t know what they will do with him but I have to say the manager there, what he has done is exceptional.
“If he is in and around the first team and training I have no doubt he will learn and improve.
“For his career I wouldn’t say he has chosen a bad club to go to, I know a lot about the club, it’s an excellent club but for his development we will have to wait and see where it goes for now.
“But he was a great lad, he tried hard, good ability, so I wish him all the best because he is a really, really nice lad, well-mannered, which is important.”