Isn't bastard child a tautology? My understanding is that bastard means "child born out of wedlock" (or at least some recognisable, formalised relationship).

The father would be a fornicator (if the neither parent was married) or an adulterer (if one of them was (or both were but not to each other)). Similarly, the mother would be a fornicatrix or an adulteress. Neither of these terms differentiate those unions that result in a child from those that don't, and I have no idea if such terms exist.