"sodomite," 1550s, earlier "heretic" (mid-14c.), from Medieval Latin Bulgarus "a Bulgarian" (see Bulgaria), so called from bigoted notions of the sex lives of Eastern Orthodox Christians or of the sect of heretics* that was prominent there 11c. Compare Old French bougre "Bulgarian," also "heretic; sodomite."
Softened secondary sense of "fellow, chap," is in British English "low language" [OED] from mid-19c. Meaning "something unpleasant, a nuisance" is from 1936. Related: Buggerly.
* The religious heretics in question were the Bogomils, whose name is a Slavic compound meaning "dear to God" (compare Russian bog "god") and might be a translation of Greek theophilos.
"to commit buggery with," 1590s, from bugger (n.). Meaning "ruin, spoil" is from 1923. Related: Buggered; buggering. Bugger off "go away" is from 1922, but the connection is obscure.