Green’s Dictionary of Slang

grinning bear n.

(US) the vulva.

1961

(con. early 1950s) J. Peacock Valhalla 118: What was that about have you ever seen a grinning bear? [Ibid.] 178: I woke up with my nose down there one night and woulda sworn to God I was staring that old grinnin’ bear right in the face.