'Bastard' is only used for men.
To say that 'bitch' is the 'equivalent' for a woman isn't entirely accurate, as the two words imply a different kind of behaviour. The reasons for this are so unpleasant, irrational and sexist that it's probably not worth looking into further.
'Bitch' is a nasty word, and I'm sure that all the other native speakers here would agree that you shouldn't use it.
Two more points about 'bastard':
1. The definition 'a child born out of wedlock' is hardly ever used in modern day English or modern contexts.
2. 'Bastard' can be offensive or non-offensive, depending on the tone of voice, context, and relationship between the speakers. While it is offensive if used in an aggressive manner, it can be used almost affectionately between friends. If one friend called another 'a lucky bastard' or 'a silly bastard', this wouldn't be offensive at all - on the contrary, it would confirm the fact that the two men were good friends.