pooh itself (as in to belittle, or pooh-pooh a notion) goes back further:
In my youth (
cried the sage!!) the use of both "pooh" and "Bah!" as interjective exclamations to express disapproval was still alive (but only just - it was likely to bring amused glances, and you were more likely to hear the terms used in fun than in earnest.)
"Pooh" is dismissive, as keiva has already ably demonstrated.
"Bah" was an ireful comment, as in:-
"Bah! Stuff and nonsense! I've never heard such rubbish in my life!"
Definitely the sort of stuff for which excalmation marks were invented.
The Gilbertian character, Pooh-Bah (Lord High Everything Else),
Hello, Jackie!!
was a haughty person with a great sense of his own worth allied to an even greater sense of the unworthiness of everybody else in the world. At one point in the opera, he traces his ancestry back to a primeaval amoeba, on the basis that only the top families can trace their family trees back more than a couple of hundred years.
He looks down on everyone else, and is dismissive of all of the ideas of the world (apart from his own ideas, or those that will bring him an immediate cash bonus!)
The name typifies the character, which is, itself, a hefty dig at the aristocratic politicians of the day (c1860s, probably - my book of G&S is downstairs and it takes too long on the stair lift to go and get it!) who were a patrician lot, and some of them were
very patronising.
As to Winnie-the-Pooh , I also have read the bit about the fly on the nose, but hadn't heard about the black swan.
