Apart from Leland, Bernstein is Kane's biggest right-hand man. In his own words, Bernstein is with Kane from "before the beginning" and he has a front-row seat to Kane's gradual fall. When asked if he knows who "rosebud" is, Bernstein can only guess,
BERNSTEIN: That Rosebud? Maybe some girl? There were a lot of them back in the early days –
This tells us that like Leland, Bernstein has some special knowledge of Kane's early days. But he still doesn't know who or what "rosebud" is.
Bernstein doesn't get much character development in this movie, but there's one great speech where he shows his sentimental side by telling the story of a girl he once saw getting off a ferry. As he tells Thompson,
BERNSTEIN: I only saw her for one second and she didn't see me at all—but I'll bet a month hasn't gone by since that I haven't thought of that girl.
He's trying to make a point about how "rosebud" could have been almost anyone that Charles Kane had ever met, but in the process he gives us some great insight into how much of a sentimental and nostalgic dude Bernstein is deep down.
He's also a guy who's not impressed by rich people, as he tells Thompson, "It's no trick to make an awful lot of money if all you want is to make a lot of money." In the end, Bernstein tells us an awful lot about Kane, even if he's never gutsy enough to stand up to the guy.