Is calling someone "bub" rude/offensive?

No, it's not rude. "Bub" is loosely taken from the word "brother". It's the same idea as calling someone "bro".

It certainly could be used in a way that's patronizing, which is what your unlikable character seems to be doing. But the word itself is not rude.

bub

bəb/

noun (NORTH AMERICAN, informal)

an aggressive or rude way of addressing a boy or man.

"hey, bub, I'm looking for someone"

is the definition I get when I google "define bub", it's likely people might not like it.

Sometimes. If it's just for fun, it's not rude. If it's someone's name, it's not rude. My neighbor's name is Barbara, and we call her Bub for short.

Wolverine also calls a lot of people "Bub."

Generally, it IS meant to be offensive.

Have a polite day.

Etiquette takes over where laws end.

No, Scott. Bub is cool.

Not unless you're Wolverine

If you're not close to them, yes.

Yes.

depends on why theyre saying it and to who theyre saying it to