One of the basic ways to measure atmospheric pressure is a bourdon, a coiled tube, always closed at one end. It can be open to changes in pressure at one end, so it will uncoil as that pressure rises*. This might remind you of the party favors with coiled paper tubes that make a buzzy whistly noise and roll out and in. Well enough; the bourdon is also a stopped pipe in an organ, known for its buzzy tone, or the lowest drone on a bagpipe.
I assumed that the pressure gauge was named after the musical uses, which are clearly older -- the gauge was patented in 1849... by Eugene Bourdon. (There's a town Bourdon in France.) One of the translations Google gives for 'buzz' in English is 'bourdonner' in French.
Which came first? It seems unlikely that a name would have moved from a scientific instrument to the bagpipe in a hundred years, but a rare coincidence that someone named Bourdon found another use for the stopped pipe. Perhaps he was familiar with the musical behavior because of the coincidence of his name; perhaps the town Bourdon has been finding all the uses there are for stopped pipes for centuries; there are French cold-air bagpipes of quite respectable antiquity.
*Or closed at both ends and reacting to surrounding pressure.