I once made a bowstring from sinew. Strip the tendon from both sides of the backbone of a deer and let it dry. Once dry, pound it with a blunt rock to break it down into fine fibers. Twist the fibers into two yarns, then counter-twist the yarns together to make a string.
When your making the yarns you'll need to introduce new fiber as other fibers peter out. Try to maintain even thickness the whole length.
When counter-twisting the yarns together you want to twist them together in the opposite direction as how you twisted the yarns. So if you made your yarns by twisting the fibers together counter-clockwise you'll now twist the two yarns together clockwise. This will cause the different twists to counteract each other, thereby creating a hold. I never was able to break this string, but after leaving it in the garage for a few years I found it covered with mold and dead ants, and disintegrated down to nothing.
Also try stinging nettle. Collect the stems (WITH GLOVES!) and dry them. Once thoroughly dry, soak the stems until supple, then pound with a blunt wooden mallet or club over a smooth wooden anvil. The woody debris inside the stems will break up, leaving long, strong fibers. Scrape the fibers clean with a smooth-edged rock by laying the fibers across the wooden anvil and scraping with the rock held perpendicular to the anvil surface.
Make your bowstring longer than the bow length to allow for tying. Roughen the tips of your bow by scraping with a rock, smear boiled pitch over the roughened area, and wrap it with sinew fibers. This will create a no-slip surface to tie your string to.
