My take on it is that she asked for a double entendre (a saying that could mean two things, the underlying, i.e. hidden. meaning most likely dirty or sexual in nature), and he:
A: gave her a saying that could mean two things, etc. (instead of a drink, his function, which is WAY nutty)
B: a drink called a "double entendre", being ignorant as to what a REAL double entendre is, or possibly jaded or confused, or acting fast on his feet, doing a bartender's job correctly (they are supposed to be able wing it)
C: a single shot instead of a double (he's a lousy bartender)
D: she's fishing for a sexual encounter and he provided a witty retort that got the ball rolling further in that regard
It is not funny in the slightest - horrible material
BTW I do not get most jokes either, but having not gotten so many I started to analyze all the things they could mean on whatever levels might be involved; needless to say I usually do not laugh at most jokes, because by the time you actually figure them out, it's more like a science experiment.
Curiously I think I could write some good material, as this is what Immanuel Velikovsky called "the bi-sociation of two events", that is, the juxtaposition of two (or more) things that do not naturally belong together, with the result that the two frames of reference being so oddly put together makes the person hearing the joke laugh (according to the theory that laughter is a response to negate fear, i.e., if these tho things WERE found together it would mean we are insane, hence afraid of this "truth".)