ooo, I saw an interesting method for cordage on Ray Mears' Bushcraft... uses Willow bark though, not cotton...
All you basically have to do is get a big willow branch (a bit thicker than your wrist, or so he said), strip the bark from it... remove the outer bark and then whack it up into fibres...
Add some ash from an old campfire or somethin' to a pot of boiling water and add the fibres from the willow bark to it. Supposed to make it stronger & more flexible.
After it's turned a brown-gray colour, take it out and dry it.
Then get your hands wet just to dampen the fibres a bit and start twisting! Start in the middle so that it gets a kink and just twist the rest from there.
Dunno just how strong it'd be... but it certainly looked like string!
Hope this helps!