The Collaborative International Dictionary of English v.0.48:

Bastardy \Bas"tar*dy\, n.
   1. The state of being a bastard; illegitimacy.
      [1913 Webster]

   2. The procreation of a bastard child. --Wharton.
      [1913 Webster]

WordNet (r) 3.0 (2006):

bastardy
    n 1: the status of being born to parents who were not married
         [syn: bastardy, illegitimacy, bar sinister]