This may not be a new idea, but I haven't seen it mentioned. I was looking around the house for paper shopping bags that would yield strips long enough to back my first bow with when I remembered that I had a good supply of paper garden waste bags in the garage. These are two-ply bags made of heavy paper, and you get get 4 foot strips from them if you're careful. They're heavier than shopping bag paper, too.
I cut wide strips, wet them, and then hung them from a convenient heater duct in my basement shop- they were wet enough to stick, and hanging there there wrinkled worked themselves out. I spread Titebond III on the limbs, applied the paper, covered that with wax paper, and clamped that to another 1x2. I wiped off the excess glue squeeze out with a damp shop rag and left it to set up overnight.
The next day I unclamped it, trimmed the excess paper with a razor blade, and gave the bow a coat of Tru-Oil. The paper took this up and darkened nicely, giving it a look not unlike tanned leather. A second coat darkened it a bit more. I'll do a few more rubbed on coats and finish up with wax, and then it's on to bow #2!