Green’s Dictionary of Slang

to retreat or withdraw, to resign.

1903		‘Hugh McHugh’ Out for the Coin 17: Bow yourself out of D.Q. & N. There are doings.
1939		G. Marx letter 24 June in Groucho Letters (1967) 20: Although we are bowing out after July 9th, there’s more than a strong likelihood that we’ll reappear in the fall.
1946		Mezzrow & Wolfe Really the Blues 38: Now every time I’d seen that screen before, it meant some poor cat was bowing out for keeps.
a.1975		Wodehouse Sunset at Blandings (1977) 22: When I found that his club was the Athenaeum, crawling [...] with bishops and no hope of anyone throwing bread at anyone, I bowed out.
2001		N. Barlay Hooky Gear 198: Farooq know the score and hes bowin out, steppin back in the yard for a smoke.
2012		E. Kurtz ‘In the Neighborhood’ in ThugLit Dec. [ebook] Little Frank bowed out. He said he had to get home to his wife.