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]

Bouvier's Law Dictionary, Revised 6th Ed (1856):

BASTARDY, crim. law. The offence of begetting a bastard child.



Bouvier's Law Dictionary, Revised 6th Ed (1856):

BASTARDY, persons. The state or condition of a bastard. The law presumes
every child legitimate, when born of a woman in a state of wedlock, and
casts the onus probandi (q. v.) on the party who affirms the bastardy.
Stark. Ev. h. t.