Online Etymology Dictionary

bloody (adj.): Old Engish blodig, adjective from blod (see blood). Common Germanic, compare Old Frisian blodich, Old Saxon blôdag, Dutch bloedig, Old High German bluotag, German blutig.

It has been a British intensive swear word since at least 1676. Weekley relates it to the purely intensive use of the cognate Dutch bloed, German Blut. But perhaps it ultimately is connected with bloods in the slang sense of "rowdy young aristocrats" (see blood (n.)) via expressions such as bloody drunk "as drunk as a blood."

Partridge reports that it was "respectable" before c. 1750, and it was used by Fielding and Swift, but heavily tabooed c. 1750-c. 1920, perhaps from imagined association with menstruation; Johnson calls it "very vulgar," and OED writes of it, "now constantly in the mouths of the lowest classes, but by respectable people considered 'a horrid word', on par with obscene or profane language."
The onset of the taboo against bloody coincides with the increase in linguistic prudery that presaged the Victorian Era but it is hard to say what the precise cause was in the case of this specific word. Attempts have been made to explain the term's extraordinary shock power by invoking etymology. Theories that derive it from such oaths as "By our Lady" or "God's blood" seem farfetched, however. More likely, the taboo stemmed from the fear that many people have of blood and, in the minds of some, from an association with menstrual bleeding. Whatever, the term was debarred from polite society during the whole of the nineteenth century. [Rawson]
Shaw shocked theatergoers when he put it in the mouth of Eliza Doolittle in "Pygmalion" (1914), and for a time the word was known euphemistically as "the Shavian adjective." It was avoided in print as late as 1936. Bloody Sunday, Jan. 30, 1972, when 13 civilians were killed by British troops at protest in Londonderry, Northern Ireland.
bloody (v.): 1520s, from bloody (adj.). Related: Bloodied; bloodying. Old English had blodigan "to make bloody," but the modern word seems to be a later formation.