Silk chiffon - and I stress the silk, because it is a better material- or a silk organza, if you'd like a bit of stiffness to it.
Another option is to look for antique veiling made of cotton Torb and Reiner out of London used to carry some, but I'm afraid they sold out, But it wouldn't hurt to check with them anyway.
EBay can often have some surprising yeilds, especially for antique patterned veiling. I got some lovely black last year.
I can help you find the materials if needed - after all, I'm a professional milliner. This is what I do for a living.