No doubt. I've already commented on Bahamaian "authenticity" elsewhere. 'Nuff said.

Joe had remarked on this particular volume in Songbook Indexing: Calypso/Caribbean Songbooks . Like vaudeville's "John B," this is just the earliest (??) documentation of the song in the Bahamas. In this context "Bid You Goodnight" is performed as a circle game/party song.

fwiw:
Sankey: "The Sweet Singer of Methodism"

The Senior Methodist Missionary to the Bahamas for most of his adult life was a fellow by the name of T.H.C. Lofthouse. His son Charles was a founder of the Bahamian goombay genre in the early 20th century. ("Bahama Mama," &c.)