I've never backed a bow with linen string, but I've backed two with flax strick (combed long-line flax). I used hide glue both times. I'm not sure if this applies when using string, but I pre-wet the material in water with a little soap added to it and blotted it to absorb any excess water prior to swirling it in the hide glue; pre-wetting the fiber made it soak up the hide glue better, and the soap in the water helped to negate the effects of the pectin in the fiber (the pectin makes it resist absorbing the glue).
Will