I’d honestly like to know approximately how many stuffed bears there are in the world. I assume that there’s no teddy census - is there some other way of coming at a good estimate?
I’ve got twelve of them: leftovers from when the kids were little’uns and a few others thrown in for good measure…dunno where they came from, but they live in my cupboard now.
One of my jobs involves flogging teddies for a charity here in Australia: I’ve spoken to many people who possess ten, twenty and sometimes MORE teddies, either as collectors, or just as poor schmucks like me who happen to ‘adopt’ them unknowingly.
From my anecdotal experience, I’d reckon there’d be more teddies than people in the world. Sorry, no cite. 
I don’t know the answer, but just wanted to add this anecdote:
One of the world’s foremost authorities/collectors of teddy bears was none other than late actor Peter Bull, best remembered as Bogey’s nemesis in “African Queen” and the Soviet Ambassador in “Dr. Strangelove.” He actually appeared in the 1980s Jack Palance “Believe It or Not!” series talking about teddy bears.
According to the Teddy Bear Museum, a member of Bull’s collection (Delicatessen, b. 1907) appeared as Sebastian Flyte’s bear Aloysius in the TV series Brideshead Revisited.
While some collectors have dozens of teddy bears, there are many, many more children than there are teddy bear collectors, so it’s probably safe to ignore the collectors. And some kids have multiples, but some don’t have any, so let’s say about one per kid. And there are some cultures where they’re uncommon, or where most people are in poverty and can’t afford luxuries like toys, so let’s say it’s just kids in the Western world. The combined population of North and South America, Europe, and Australia is about 1.7 billion. Of those, let’s say that about a quarter are children, for about 420 million teddy bears in the world.
Sounds like somebody just did a job interview! 