The most interesting thing about the Quayle comment was that it was a lie. Bentsen was not close to JFK in any way. He was just a fellow senator and nothing more. It was a truly shameless cheap shot.
It looks like Bentsen and Kennedy served in the House together for two terms between 1949 and 1953, but Bentsen didn't run for Senate until 1970. I have no idea how friendly they were, but as young members of the House elected only two years apart, one would assume they were at least on speaking terms.
Quayle set himself up for Bentsen's comment. Not only that, but he had been doing so in previous speeches, so the Democrats could plan for it. It was a stupid thing to do in a national campaign.