Green’s Dictionary of Slang

to sleep, thus adj. asleep (see cite 2001).

1944		C. Fluck ‘Bubbles’ of the Old Kent Road 26: I’m off to Bo Peep and in the morning I’ll make Chummy a cup of Rosy Lee.
1957		G. Kersh Fowlers End (2001) 131: To Bo-peep on their rolling billows [...] Where their loaves o’ bread repose.
1965		Minneapolis Star (MN) 9 Feb. 32/1: I said ‘ta ta’ and was glad to get home to bo-peep.
1969		S.T. Kendall Up the Frog 13: I got ’im right on the Gunja Din with me Oliver Twist an’ put ’im to Bo-Peep.
1976		(ref. to 1930s) R. Barnes Coronation Cups and Jam Jars 75: I goes out in the kitchen, after making sure he’s gone well to Bo Peep.
1982		G. Newbold Big Huey 245: bo-peep (adv) Asleep.
1998		C. Fitzpatrick ‘Gower ’98’ on Sussex University Canoe Club 🌐 So to round the night off, the chief of the battle cruiser let us bo peep in the near and far. Well those of us not in a chalet or peter pan. What a top bushel of coke.
2001		D. Looser Boobslang [U. Canterbury D.Phil. thesis] 27/2: bo peep adj. asleep.