The Collaborative International Dictionary of English v.0.48:

Bagnio \Bagn"io\, n. [It. bagno, fr. L. balneum. Cf. Bain.]
   1. A house for bathing, sweating, etc.; -- also, in Turkey, a
      prison for slaves. [Obs.]
      [1913 Webster]

   2. A brothel; a stew; a house of prostitution.
      [1913 Webster]

WordNet (r) 3.0 (2006):

bagnio
    n 1: a building where prostitutes are available [syn:
         whorehouse, brothel, bordello, bagnio, house of
         prostitution, house of ill repute, bawdyhouse,
         cathouse, sporting house]
    2: a building containing public baths [syn: bathhouse,
       bagnio]