This word — meaning to speak pompously — is almost entirely restricted to the United States; it doesn’t appear in any of my British English dictionaries, not even the big Oxford English Dictionary or the very recent New Oxford Dictionary of English. Yet it has a long history.
It’s most closely associated with U S President Warren Gamaliel Harding, who used it a lot and who was by all accounts the classic example of somebody who orates verbosely and windily. It’s a compound of blow, in its sense of “to boast” (also in another typical Americanism, blowhard), with a mock-Latin ending to give it the self-important stature that’s implicit in its meaning.
The word is actually much older than Harding; Fred Shapiro of the Yale Law School has recently turned up several examples from the middle of the last century, such as this one from the Debates and Proceedings of the Convention for the Revision of the Constitution of the State of Ohio in 1851: “The bloviators attempt to disturb the proceedings of this Convention”. This and other examples suggest it was at first a local word in Ohio, Harding’s home state. Bloviate may be a back-formation from the noun bloviation. This would fit with the US fashion in the early nineteenth century for expansive mock-Latinate words like sockdolager, hornswoggle and absquatulate.
There’s a gap in the citation record in the middle years of this century. The word only began to be used again in the 1960s, even then at first always in reference to Harding. This may be linked with a number of biographies of him that appeared about that time. The word only returned to any sort of regular use in the nineties.