Matters have not been helped by Mark Bowen's defection from St Andrew's to become assistant manager at Rovers - Bruce and Bowen no longer speak.
Birmingham's boss said: "I don't think I'll be invited in for a drink, do you? I'll shake hands with Mark (Hughes), no problem, and wish him all the best, but it's not just Sav there's a problem with, is it?"
On the tension with Savage, Bruce added: "Robbie shook my hand and apologised.
"He was disappointed about the way it ended. And he was man enough to say he wished it hadn't finished like it had.
"We lost a very good player. He was a hero to our supporters and we shared some good times together. He was absolutely adored by our fans and I don't care what you say, he wasn't going to get that at Blackburn.
"Do I think it was the wrong move? That's not for me to say. But when I heard he broke his leg last season, I did feel for him. I don't know whether he has matured. You will have to ask Sav, that, but injuries like that put things into perspective for you. And like they say, time is a great healer."