Meaning "to leave," usually used at the end of a conversation. Originates in the idea of "plopping down" on a horse in order to ride back to one's home. "Down" is usually eliminated, although on occasion it is heard.
Joe: ...and then Barb told me that the bricks had been there the whole time.
Jim: Interesting. Well, it's getting pretty late--it's probably time for me to plop on the horse.
Joe: All right, see you later.
Jim: Yup, goodbye.