Buxton martini Share definition Flag Gourmet cocktail. A PBR or Busch Light draft with an olive. Enjoyed by people in Maine and named after a town in the state. Bartender: What ah ya havin’ bub? Patron: I’ll have a friggin’ Buxton martini, two olives. Buxton martini by MaineMan207 December 22, 2022 Get the Buxton martini mug.