Green’s Dictionary of Slang

burley n.1

also burly
[abbr.]

(US) a burlesque show, a striptease show; usu. attrib.

[US]Weseen Dict. Amer. Sl.
[US]H.M. Anderson Strip Tease 15: ‘The rough stuff was what made burly tick’.
[US]S. Sterling ‘Ten Carats of Lead’ in Black Mask Stories (2010) 227/2: Claims she’s a showgirl. used to be in burly.
[US]J.E. Dadswell Hey, Sucker 100: burly show ... a burlesque attraction.
[US]H. Robbins Dream Merchants 44: We pay you more here for one day’s work than you make all week hustling your ass on a burley line!
[US](con. 1911) Green & Laurie Show Biz from Vaude to Video 61: Variety described it as ‘a burly show of the highest type’. [Ibid.] 75: The great John L. had his own John L. Sullivan Players in 1907. ‘He’s with burly,’ Variety reported, ‘and keeping sober.’.
[US]D. Dressler Parole Chief 201: Sue moved to a bigger and better burley house, eventually became a stripper of sorts.
[US]‘Curt Cannon’ ‘The Death of Me’ in I Like ’Em Tough (1958) 115: She might have been on the runway of a burley house.
[US]H. Ellison Rockabilly (1963) 130: It was gutty, almost burley bump-&-grind treatment with every whump!
[US]S. Longstreet Flesh Peddlers (1964) 197: He was always a top banana in burly.
Weekly Wire 20 July 🌐 To begin with, there is that odd, burley show cliche woven into the title: a clarion blast of coarse nonsense that dissipates all fears of academic timidity or lofty cultural pretensions.
Gambit Weekly 18 June 🌐 But also because it lends itself to a cool, concupiscent display of tits and ass – like a burley show conceived by Andy Warhol, with his trademark warmth and effusiveness.