1857, American English, a Midwestern word for "to talk aimlessly and boastingly; to indulge in 'high falutin'," according to Farmer (1890), who seems to have been the only British lexicographer to notice it. He says it was based on blow (v.1) on the model of deviate, etc.
It seems to have been felt as outdated slang already by late 19c. ("It was a leasure for him to hear the Doctor talk, or, as it was inelegantly expressed in the phrase of the period, 'bloviate' ...." ["Overland Monthly," San Francisco, 1872, describing a scene from 1860]), but it enjoyed a revival early 1920s during the presidency of Warren G. Harding, who wrote a notoriously ornate and incomprehensible prose (e.e. cummings eulogized him as "The only man, woman or child who wrote a simple declarative sentence with seven grammatical errors") at which time the word took on its connection with political speech; it faded again thereafter, but, with its derivative, bloviation, it enjoyed a revival in the 2000 U.S. election season that continued through the era of blogging.