"B.A.Y." represents "The Brotherhood of American Yoemen", a lodge/fraternal organization that Frank and Sophie belonged to.
In 1983 I was in Franklin County visiting relatives and seeing places of my family history, and found Champion City and the hall. The town of Champion City in 1983 consisted of two abandoned lodges - B.A.Y. and Modern Woodmen of America - a general store, and a Methodist Church up on the hill, overlooking the Bourbeuse River.
Hay had been recently stored in the old frame building when I visited, but there were still backless benches in it. The hall was one large room, with a fireplace in the end wall opposite the entrance. There were two small rooms on the right and left of the entrance. There were signs above the doors to the small rooms; "Ladies" and "Men". Since there was no evidence of a bathroom, and surely the out house had been out back, these must have been "rest rooms" - small changing rooms.
Sophie's sister Ida Drewel Lake told me in the 1980's: "After the dance, the couple went back to Sophie's parent's house and were greeted by a shivaree. All the neighbors came from far and wide and brought crazy old shotguns and shot into the air, and whooped it up. Well anyway, one of those old buggars got upstairs and into one of the two sleeping rooms and got to messing around and broke out a window. That made Dad (Louis Drewel) mad because glass was hard to get a hold of. And they had to get someone up there that night to nail in the window because it was so cold, being February."
Sounds like it was an eventful day!