Bombinate sounds like it should be the province of bombastic blowhards who bound up and bombard you with droning blather at parties—and it is. The word traces back to the Greek word bómbos, a term that probably originated as an imitation of a deep, hollow sound (the kind we would likely refer to as “booming” nowadays). Latin speakers rendered the original Greek form as bombus, which led not only to bombinate, but also to bomb, bombard, and bound (“to move by leaping”).
borrowed from Medieval Latin bombinātus, past participle of bombināre, word of uncertain meaning formed from the base of Latin bombīre or bombilāre "to buzz, hum" (in New Latin taken to be synonymous with these words), derivatives of bombus "buzzing, humming," borrowed from Greek bómbos — more at bomb entry 1
Latin bombināre has had a shadowy existence from the time of Martianus Capella (5th century c.e.), who uses the agent derivative bombinātor in his De Nuptiis Philologiae et Mercurii. The 11th century lexicographer Papias glosses bombināre as conuiciari ("to utter abuse against, scold, revile"), or at least Papias is thus recorded in an early printed edition (Venice, 1485), which was picked up in Du Cange's dictionary of post-classical Latin, Glossarium mediae et infimae Latinitatis. An oft-quoted occurrence is in the imaginary book title Quaestio subtilissima, utrum Chimaera in vacuo bombinans possit comedere secundas intentiones ("A subtle question, whether a Chimera buzzing in a vacuum can devour secondary intentions"), part of a mock library in François Rabelais's Pantagruel (the first volume, printed ca. 1532, of the Gargantua and Pantagruel novels); the translation of bombinans is conventional, but Rabelais' meaning is far from certain.