In the book, he isn't very upset by Frodo's alarming disappearance because he knows people will be discussing it over a pint for years to come. Boromir presents another opportunity to sell more beer. Though Barliman is easily flustered and not always the quickest on the uptake, he is a savvy businessman.
But now I am imagining open mic night at the Pony. Dwarven karaoke. Hobbit poetry slams. Rangers playing six-string guitar.