Bloody - One of the most useful swear words in English. Mostly used as an exclamation of surprise i.e. "bloody hell" or "bloody nora". Something may be "bloody marvellous" or "bloody awful". It is also used to emphasise almost anything, "you're bloody mad", "not bloody likely" and can also be used in the middle of other words to emphasise them. E.g. "Abso-bloody-lutely"!
I always have assumed the reasoning and origin behind the term "bloody" was to do with "Christ's blood"... therefore the blasphemous element is what makes it offensive... I believe that Shakespeare would use the terms "'swounds" as a cleaner version of "Christ's wounds" and "'sbloods" as a cleaner version on "Christ's blood"... but that is not so...
According to the Oxford English Dictionary:
"In foul language, a vague epithet expressing anger, resentment, but often a mere intensive, especially with a negative -- as, not a bloody one." They cite an 1840s usage.... On the other hand, the use as adverb dates back to 1650s: as an intensive, meaning, "very" or "and no mistake". In the 1880s, it was considered a "horrid word" by respectable people, on par with obscene or profane language, and was printed in newspapers, etc., as "b----y."
The OED says the origin is uncertain, but possibly refers to "bloods" (aristocratic rowdies) of the late 17th-early 18th centuries ... "bloody drunk" arising from '"drunk as a blood" ... and the association with bloody battle, bloody butcher, etc., "appealed to the imagination of the rough classes." They add, "There is no ground for the notion that 'bloody', offensive as ... it is now to polite ears, contains any profane allusion or has connection with the oath ' 's blood!', referring to the blood of Jesus."
As to how offensive the word actually is, well, that depends on whom you ask, or say it in front of. It's fair to compare it to the "F-word," in that it may cause your grandmother to faint, but may cause scarcely a raised eyebrow amongst the gang at the pub.
On a scale of 1-5... (where 1-5 are swear words that you wouldn't utter in front of children) I'd rate "bloody" in modern day Britain as a 1/2 (but still not utterable in front of children... especially from a teacher.) A similar level of offence can be assigned to the terms "bugger" and "damn."