I have a co-worker who keeps referring to someone on the telephone as “J.B.” Every time I hear her say it, I always think of a rich man in a top hat, a banker from the twenties or thirties or such. Why are rich men in the movies often called “J.B”?
The iconic American financier you’re describing isn’t a J.B., but a J.P.: John Pierpoint Morgan, who formed General Electric and U.S. Steel, and is one of the most significant figures in the history of American finance.
I think using either J.P. or J.B. in naming a rich character is an allusion to J.P. Morgan, and in an earlier era would have automatically conjured up his image. I know that when I hear J.P., I still think of him first. Here’s a picture of J.P. Morgan, and his son, J.P. Morgan, Jr., showing the iconic image.
“J. Pierpont Finch, that’s F-I-N-C-H.”
Great. Now the rest of the day I’ll be going, “J. Pierpont…Rosemary…and for the rest of my lifetime program, give me more of the same…” 
Name three. Heck, name one. I can’t think of any off the top of my head.
John Wayne in The Shootist… J.B. Books
ETA: Not stunningly rich though I suppose.
There was also J.D. Rockefeller. Not a J.B., either but… close?
Not a movie, but I remember an ad for McDonald’s, I think, from the 80’s, probably, wherein the venerable corporate chairman J.B. daydreams about French fries, or some such, during the board meeting while the other directors labor in vain to bring him back to here and now.
He was already technically rich, but it was during his brief fantasy of being a Hollywood agent that Jethro Bodine of the Beverly Hillbillies had Elly May (playing his girl Friday) answer him, “Yes J. B.” I never thought it had to do with anything other than his actual initials.
I don’t know where it comes from but I imagine some toady in a black and white show or movie saying to his Boss “Great Idea J.B.!” “That’s another winner J.B.!” etc. I have made the same joke based off this memory. But yeah, I have no idea where it comes from.
ETA: it’s very possible this comes from the Beverly Hillbillies episode referenced above.
Is everyone unaware of J. B. Biggley? (ETA: And yet there were refs to the musical HTSIBWRT in this thread!)
Maybe not a super-rich man in that particular realm, but probably on his way. Of course FINCH would no doubt become even richer in the long run. 
OK, this might help displace that:*
Stand, Old Ivy, stand firm and strong
Grand Old Ivy, hear the cheering throng
Stand, Old Ivy and never yield
Rip, rip, rip the chipmunk off the field*
Oddly, a search of characters in IMDB list only one: J. B. Baker, in the TV series LA Firefighters.
Somebody refresh my memory here!
Over the weekend I vaguely recalled the origin and first appearance of Captain Boomerang from a reprint in a Giant Annual comic some time after I started to buy and collect my own comics. (This, BTW, was the same summer as the Rochester riot.) It seems to me that while CB was already planning to start a one-man crime wave using boomerangs, a big exec proposed the idea of selling boomerangs as toys, using an already-skilled operator as human “mascot” and spokesman.
The exec was surrounded by the most obvious yes-men you could imagine, and whether or not they would have spontaneously been enthused by such an idea, the air was filled with congratulatory agreement.
I seem to recall that the “great idea” and similar phrases were followed by “J.B.” although I suppose I could be remembering wrongly.
… because FUTBOL!
FUTBOL!
is formerly known as…
Trans Fat Og, who in turn was once…
True Blue Jack… and the “Jack” later became an eleventh-hour nickname in 3D for clarity in board meetings, and my legal first name is John…
and if you must know, my real initials are…
wait for it…
J.B.!!!
J seems to be a common initial in general, at least where the media is concerned. One reason could be that the initial stands for John, and the character wanted to differentiate themselves from all the other Johns out there, but even without that stipulation you have:
Homer J. Simpson
Bartholomew J. Simpson
Abraham J. Simpson
Sabrina J. Spellman
Philip J. Fry
J.R. Ewing
J. Jonah Jameson
Dr. John “J.D.” Dorian
These are all references to Rocky & Bullwinkle. Rocket J. Squirrel and Bullwinkle J. Moose were middle-named after Jay Ward, who created them. I suspect at least a few other fictional characters got their middle names from Rocky and Bullwinkle, or from Homer and Bart.
I used to work with a clown who went by “J.B.” and was the most full-of-shit person I have ever met. Actually, everyone at work agreed on that.
I called him “Jurassic Bullshit”.
When I hear “J.B.”, I cringe.
Cool trivia, thanks.
I assumed it was because it’s a letter that sounds good and distinctive. Strong consonant start, with an “ay” sound to finish it off. But maybe that’s just me.
The only J.B. I’ve ever heard of is Priestley. And he wasn’t particularly wealthy.