bleeding n.

Old English bledan, "cause to lose blood, to let blood" (in Middle English and after, especially "to let blood from surgically"), also (intransitive) "emit blood," from Proto-Germanic *blodjan "emit blood" (source also of Old Norse blæða, Dutch bloeden, German bluten), from PIE *bhlo-to- "swell, gush, spurt," or "that which bursts out," from suffixed form of root *bhel- (3) "to thrive, bloom."

The meaning "extort money from" is from 1670s. Of dyes or paints, "to wash out," from 1862. Figuratively, of the heart, "suffer anguish, feel pity or sorrow," late 14c.

"of the nature of blood, pertaining to blood, bleeding, covered in blood," Old English blodig, adjective from blod (see blood (n.) + -y (2)). Common Germanic, compare Old Frisian blodich, Old Saxon blôdag, Dutch bloedig, Old High German bluotag, German blutig. The English word is attested from late 14c. as "involving bloodshed" and by 1560s as "bloodthirsty, cruel, tainted with blood-crimes."

It has been a British intensive swear word at least since 1676. Weekley relates it to the purely intensive use of the cognate Dutch bloed, German Blut. Perhaps it is influenced by bloods in the slang sense of "rowdy young aristocrats" (18c., see blood (n.)), via expressions such as bloody drunk "as drunk as a blood," and it might be ultimately from the general association of the blood and high emotions and heated passions.

Partridge reports that bloody was "respectable" before c. 1750, and it was used by Dryden, Fielding and Swift, but it was heavily tabooed c. 1750-c. 1920. 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" (1913), 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, saw 13 civilians were killed by British troops at protest in Londonderry, Northern Ireland.

name applied to several types of flowering plant, 1690s; see bleeding (adj.) + heart (n.).

In the American English sense of "person liberally and excessively sympathetic" (especially toward those the speaker or writer deems not to deserve it) is attested by 1936 in the work of popular conservative newspaper columnist Westbrook Pegler (1894-1969), who first used it in reference to his own feelings about the Republican Party but by 1938 regularly deployed it against the Roosevelt administration and also as a modifier (bleeding-heart liberal) in his "Fair Enough" column: 

And I question the humanitarianism of any professional or semi-pro bleeding heart who clamors that not a single person must be allowed to hunger, but would stall the entire legislative program in a fight to jam through a law intended, at the most optimistic figure, to save 14 lives a year. ["Fair Enough," in Freemont (Ohio) Messenger, Jan. 8, 1938]

Bleeding in a figurative sense of "generous" is attested from late 16c., and the notion of one's heart bleeding as a figure of emotional anguish is from late 14c.; the exact image here may be the "bleeding heart of Jesus."