Green’s Dictionary of Slang

bishop’s nose n.

[var. on parson’s nose under parson n.]

(US) the rump of a chicken, duck, goose or other poultry.

[US]Reno (Nev.) Eve. Gazette 28 Apr. 2/2: The rump of a fowl is the ‘pope’s,’ ‘parson’s’ or ‘bishop’s nose.’.
[US] in DARE.
Chicken Rice Haven [Internet] 1. Wash chicken. Remove excess fat from the chicken (esp. from around the Bishop’s Nose).