How do you think Herman E. Calloway and Jimmy feel when they hear Bud’s announcement?

I believe this question is asking about the announcement that Bud makes at the end of chapter 12. This is the point in the book that Bud finally states that he believes that Herman E. Calloway is his father.

Ah the men looked over at the drummer. He stopped tapping.
He said, "Awww, man. Look, this child ain't no kin of mine. What's your momma's name, boy?"
I said, "You ain't my daddy." I pointed right at Herman E. Calloway's big belly. "You know it's you." All the eyes jumped over on Herman E. Calloway. He quit smiling and looked at me a lot harder, like he was really noticing me.

Both Jimmy and Calloway are feeling shocked and incredulous. They simply can't believe that a boy would walk in, believing the Calloway was his father. Either that, or they can't believe the boy actually believes that he can sell the story. Near the beginning of chapter 13, Jimmy makes it really clear that Calloway simply cannot be Bud's father.

Bud, you got to understand Mr. Calloway here can't be your daddy, no how, no way, nuh-uh. I don't know what gave you that idea, but whatever, we've got to get you back home.

Calloway may come across as gruff and rude, but the statement is a testament to the man's character. The band members know without a doubt that Calloway is not the kind of guy to father illegitimate children and/or walk away from his responsibilities. For Calloway's part, he knows Bud is wrong, and he doesn't feel the need to entertain Bud any longer.
It is possible that the announcement that the question is asking about is Bud's announcement about his mother's name.

I screamed at him, "Angela, sir." I was so mad that I hadn't meant to say "sir" but it came out anyway. "Her name is Angela Janet Caldwell."
Mr. Jimmy said, "Lord have mercy... ."
Herman E. Calloway's pipe dropped out of his mouth and he stumbled and fumbled into Grand Calloway Station, feeling his way like he'd been struck blind.

Jimmy and Calloway still feel incredulous at this point, and they are probably still filled with disbelief; however, it is disbelief that the truth is what it actually is. Bud is Calloway's grandson from his long lost daughter. There is probably a confusing mix of sadness, grief, regret, joy, and relief all going through Calloway's mind, as well as everybody else's mind in the band.