1758, "sleeping-berth in a vessel," later in a railroad car, etc., probably a shortened form of bunker (n.) in its sense of "seat." Bunk-bed (n.) attested by 1869.
"nonsense," 1900, short for bunkum, phonetic spelling of Buncombe, a county in North Carolina. The usual story (attested by 1841) of its origin is this: At the close of the protracted Missouri statehood debates in the U.S. Congress, supposedly on Feb. 25, 1820, North Carolina Rep. Felix Walker (1753-1828) began what promised to be a "long, dull, irrelevant speech," and he resisted calls to cut it short by saying he was bound to say something that could appear in the newspapers in the home district and prove he was on the job. "I shall not be speaking to the House," he confessed, "but to Buncombe." Thus Bunkum has been American English slang for "nonsense" since 1841 (it is attested from 1838 as generic for "a U.S. Representative's home district").
MR. WALKER, of North Carolina, rose then to address the Committee on the question [of Missouri statehood]; but the question was called for so clamorously and so perseveringly that Mr. W. could proceed no farther than to move that the committee rise. [Annals of Congress, House of Representatives, 16th Congress, 1st Session, p. 1539]
"Well, when a critter talks for talk sake, jist to have a speech in the paper to send to home, and not for any other airthly puppus but electioneering, our folks call it Bunkum." [Thomas Chandler Haliburton, "Sam Slick in England," 1858]
"to sleep in a bunk," by 1840, originally nautical, from bunk (n.1). Hence "to occupy a bed." Related: Bunked; bunking.