How offensive is the word Bastard? And when did it become more of an offense than a term used for child out of wedlock?
Bastard is a very old term of French origin. The way we use is today as a general term of offence is from 1830:
"illegitimate child," early 13c., from Old French bastard (11c., Modern French bâtard), "acknowledged child of a nobleman by a woman other than his wife," probably from fils de bast "packsaddle son," meaning a child conceived on an improvised bed (saddles often doubled as beds while traveling), with pejorative ending -art (see -ard).
Not always regarded as a stigma; the Conqueror is referred to in state documents as "William the Bastard." Figurative sense of "something not pure or genuine" is late 14c.; use as a vulgar term of abuse for a man is attested from 1830. As an adjective from late 14c. Among the "bastard" words in Halliwell-Phillipps' "Dictionary of Archaic and Provincial Words" are avetrol, chance-bairn, by-blow, harecoppe, horcop, and gimbo ("a bastard's bastard").
Bastard is an offensive expression but it can be used, with care, as a jocular expression:
(informal, offensive) an obnoxious or despicable person
(informal, often jocular) a person, esp a man: lucky bastard
(informal) something extremely difficult or unpleasant: that job is a real bastard.