out of the fabrics, i have always used silk, i guess mostly cos i just liked the idea of it
however i have seen many folk build bows with that polyester tape thats used for drywalling.
i agree with wolf, we use so many synthetic glues, and electricity to power our tools etc, but i guess we just have to do what we feel comfortable with.
anyway, i thought i had better do some very quick research, and found this.
however my first choice of backing would be thin rawhide, and Roy's suggestion is excellent