There is a line in the short story, A Thousand Dollars, where one of the characters is described in the statement above. My first thought was that it meant that the character was showing no interest (because Bees like honey and not vinegar) but I feel that that thinking is flawed.
So, what does it mean?
Best Answer
In popular imagining (and perhaps in real life), bees, wasps, and flies are attracted to honey but repelled by vinegar. Hence the saying "You can catch more bees [or wasps or flies] with honey than with vinegar."
In keeping with this understanding of the preferences of bees, the character Old Bryson in O. Henry's short story "One Thousand Dollars" (written circa 1905) views the affairs of Bobby Gillian with as little interest as a bee would have in viewing a cruet of vinegar. This is why, two paragraphs before the vinegar cruet simile appears, Old Bryson urges Gillian to take his as yet untold story off to the billiard room, where Gillian might find an interested audience.
The only complicating factor here is that O. Henry frames Old Bryson's reaction in neutral/positive terms (he is described as "showing as much interest as a bee shows in a vinegar cruet") rather than in negative terms ("showing no more interest than a bee would show in a vinegar cruet"). Presumably the author liked the misdirection and formal ambiguity of his formulation, which leaves to the reader the task of judging how much interest a bee is likely to have in a vinegar cruet, without explicitly stating that it is very little interest indeed.