I think you’re going to have a problem getting much of a frayed edge along a bias edging. The bias cut will facilitate going around curves, but cutting on the diagonal won’t create the frayed edge you’re looking for. The fibers will no longer parallel the edge, leading to minimal fraying. Think of a plain cotton fabric. it is easy to tear in a straight line with the grain. Tearing it leaves a nice frayed edge parallel to the original. If you cut it on the diagonal (bias), you are left with fibers coming to a V on the edge. Even if you could make it fray it wouldn’t be even or pretty. The advantages of using bias edging are it’s ability to handle curves and it’s resistance to fraying.
If you don’t need to curve it, use a straight edging.