is this bow from a red oak stave or board?
is there an issue with the back and is that why you are thinking of backing it?
if you do back it i recomend doing it at floor tiller stage.
you can us e alot of differant things as a backing.
you can use a brown grocery bag,silk,linen,cloth,rawhide sinew,cherry bark(always cool looking),snake skins,another wood or bamboo and many more.
depending on the backing you use,would determine the process of how to do it.