late 15c. (buzzing is from late 14c.), echoic of bees and other insects. Aviation sense of "fly low and close" is by 1941 (see buzz (n.)). Related: Buzzed. To buzz off "go away quickly" (1914) originally meant "to ring off on the telephone," from the use of buzzers to signal a call or message on old systems. As a command, it originally would have been telling someone to get off the line.
"a busy rumour" [Rowe], 1620s (earlier "a fancy," c. 1600), figurative use from buzz (v.). Literal sense of "a humming sound" is from 1640s. A "buzz" was the characteristic sound of an airplane in early 20c.; hence verbal sense "to fly swiftly," by 1928; by 1940 especially in military use, "to fly low over a surface as a warning signal" (for example that target practice is about to begin):
The patrol aircraft shall employ the method of warning known as "buzzing" which consists of low flight by the airplane and repeated opening and closing of the throttle. [1941 Supplement to the Code of Federal Regulations of the United States of America," Chap. II, Corps of Engineers, War Department, p. 3434, etc. ]
Meaning "pleasant sense of intoxication" first recorded 1935. The children's game of counting off with 7 or multiples of it replaced by buzz is attested from 1864 and is mentioned in "Little Women" (1868). To give (someone) a buzz (by 1922) is from the buzz that announced a call on old telephone systems (1913). Buzz bomb "V1 rocket" is from 1944.