GaryL,
One layer will be fine. Glue and the linen weight would be excessive with several layers. Slows the bow down.
If you heat treat the bow, you should wait until after heat treating to add the linen layer. Heat affects glue.
A real bad rupture on a bow limb can still split through linen, violently, and silk. However, all backing protect a bow if you live in a rocky area, and that is one reason I use backing on most.
Linen I have smoothed out with my hand, watching for air bubble and smoothing, until the glue, Titebond III, starts to set.
Keep us posted on your build.