This is an awful lot like the "How many piano tuners in Boston?" question.
So I'll make up some numbers. Let's say that 1 in 20 US teenagers want to make music. 350 million teenagers and former teenagers (including the deceased born after 1940), 17 million musicians.
Let's say that 1 in 20 musicians want to play the bass at some point. 900,000 wannabe bass players.
Let's say that 1 in 20 bass players stick with it. 50,000 actual bass players.
Let's say that actual bass players collect an average of 5 basses. 250,000 basses.
So, in the US alone, that's 850,000 (wannabes) + 250,000 (collectors) = 1,100,000 basses in the US.
The US is about 10% of the world, so 10 million basses in the world.
Every one of those figures is wrong, but I'll stand by the final result. There are 10 million basses in the world, ±100%.
So, we have another Physicist in our midst, and now have a "Drake equation" for the amount of bass players in the world. I think the piano tuners question that Fermi asked was usually quoted for Chicago, but...Boston, Chicago, no big deal.
Someone previously estimated 1 billion. That would mean one of every 7 people in the world has a bass, which seems pretty high. 10 million means 1 in every 700 people in the world has a bass. That may be low, but I'd also guess its; not too far off. The assumption that the world looks like the US is probably wrong (we probably have more basses per capita than the average), but as often happens in these things, that error is offset by the fact that we're not 10 percent of the world - more like 4 percent at this point.
One thing that is clear - if you go to Guitar Center, you can clearly tell that, even though you typically see 2 guitarists on a stage with one bass player, there are a lot less than half as many bassists as there are guitarists - the number of basses on the walls suggests that the bass market is smaller (probably much smaller) than what you'd expect by looking at a stage. That also jives with the gigs I play - when a worship leader finds out I'm available for a gig, I'll get booked for that date right away. The guitarists get booked much later - there are plenty of them to go around, no rush to sign them up early.
