just find a nice dead chokecherry/pin cherry/flowering cherry (not black cherry, the bark is unsuitable), cut off the bark in a large sheet. You must orient the bark with the lenticels parallel to the bow back, this is the direction the bark is strongest in(side to side on the tree, not up and down) The larger the tree, the more gnarly the bark (you want smooth bark), so its likely that you'll have to use several pieces to back a bow since the length of the pieces is determined by the diameter of your tree.
Scrape both sides of the bark to prepare it for gluing and to uncover that beautiful burgundy color. Cut to shape, and glue with titebond or the wood glue of your choice. Wrap down with string to keep it clamped. I'd advise only backing bows with very low crown, as cherry bark gets quite brittle when dry and will probably crack with a high crown, happened to a mini-bow I backed with bark.
here's the mini-bow in question
