I'm not entirely sure who said it and which episode. I thought it was from Homer at the Bat and involved Wade Boggs and Barney. From what I remembered the bit was something like this.

Barney and Wade Boggs are sitting at Moes.
Barney: I'm a big fan of yours?
Boggs: You like baseball?
Barney: Baseball?

But I looked online and I don't think its from the episode. Does this ring any bells for anyone? thanks-

Haven't seen it, but this says that episode is the only one Boggs appears in.

http://simpsons.wikia.com/wiki/Wade_Boggs_(character)

I like the one with Barney's movie.
He is sitting next to a woman and he belches in his usual way.

The woman asks "what crawled inside of you and died?"
He responds with, "It didn't die."

Yeah, the exchange between Barney and Wade Boggs was in regards to who was the greatest Prime Minister in the history of England.

"Lord Palmerston!"
"Pitt the Elder!"

The exchange you're thinking of might be between Barney and David Crosby.

It's in the episode "Homer's Barbershop Quartet" from Season 5. The Be Sharps won the Grammy for Outstanding Soul, Spoken Word, or Barbershop Album of the Year, and David Crosby presents the award to them.



Barney: David Crosby? You’re my hero!
David Crosby: Oh, you like my music?
Barney: You’re a musician?

Yes! that was it thank you!

He didn't belch, he was talking to her after overhearing her compliment his short film.

A woman watching the short film is moved.
Woman: It's brilliant: savagely honest, tender... he has the soul of a poet.
Barney: You're very kind.
Woman: Excuse me, did something crawl down your throat and die?
Barney: It didn't die!