In a moment of idle curiosity, I wondered whether you could make a practical (historic) bellows without tanned leather or woven cloth. It occurred to me that perhaps you could use something already flexible that did not need not some days-long chemically complex tanning process nor a tight warp loom to produce.
How about an animal bladder? I know they were used for two purposes in-period: as a bag for light items by the first peoples of North America, and as a balloon by dark ages Europeans. Are they large enough? Robust enough? Anyone ever heard of a bladder-based bellows?
Any other ideas are welcome: any animal, vegetable, or mineral alternative to tanned leather and cloth is a possibility.
Period references are of course extremely welcome. Please! Inform me!