early 15c., "catapult, military engine for throwing large stones" ("The name generally given in Europe to the cannon during the 1st century of its use" - Century Dictionary), from Old French bombarde "mortar, catapult" (14c.), from bombe (see bomb (n.)). The same word, from the same source, was used in English and French late 14c. in reference to the bass shawm, a low-pitched bassoon-like musical instrument, preserving the "buzzing" sense in the Latin.
1590s, "to fire heavy guns," from French bombarder, from bombarde "mortar, catapult" (see bombard (n.)). Meaning "attack with heavy ordnance" is from 1680s. Figurative sense "assail persistently" is by 1765. Related: Bombarded; bombarding.