Next, you have to work the bladder continuously while it is drying. If you used the soap method, grease it with animal fat, dunk it in soap solution, rinse again, work again. By now it should be possible to squeeze water easily right through the skin. If it isn't sof or if you have hard spots moisten and work while drying agin until you are satisfied. Buckskin is then smoked to improve its durability and appearance.
Green hardwood is the preferred smoking source.
A buckskin takes 1 or 2 days to smoke. I am not sure that it would be necessary or desirable to smoke the bladder if the point is for it to be elastic. Since you have 6, you could try different recipes to see if any of them work. Obviously not medieval, but the best I could do. I could feel a membrane with a little more solidity deeper inside the mass, so I figured this was the bladder.