I thought about this and I can’t say right now whether I agree or disagree.
“More air” only occurs if an expanded bladder shrinks. If the bladder is inflating or staying the same size, there is no additional air flowing through the reeds. I don’t know about the B24; on my M37C, the bladder can stay inflated or even increase in size while playing.
Originally, I thought the bladder might provide more pressure, but I think I convinced myself you can actually get higher pressures with a rigid case than with a bladder. Or, at least, the same pressure (at some point, the lungs become the limiting factor).
The bladder expands the available air. But then, why not just start with a larger rigid air chamber?
I think the complete explanation might prove a bit more complicated than one might think. The main characteristics of the bladder are that, if your blowing pressure drops, it delays a pressure drop and that, if your blowing pressure increases, it delays the increase. In other words, it smooths out pressure changes.
This may not be how it works, it’s just the only explanation that fits in with the rules of physics that I know. And, if I understand the rules properly, I’m not sure why smoothing the pressure changes would be useful for a bass melodica.
If I had a B24, I could test this by using my airbrush. I’d feed it a constant flow while holding a key down. If my theory is correct, the note would sound quiet and then get louder as the bladder filled. Then I would reduce the flow. Again, my theory would say that the volume would stay steady for a bit, then drop.
If it behaved some other way, I’d need a new theory, of course. 🙂