I make a 2-inch bias strip, folded in half.
I stitch a scant 1/4-inch seam on the front, fold to the back and do hand stitching on the back side. The front has a more finished look. Never even considered sewing to the back and folding to the front!
Obviously, if you do a 3/8-inch seam you'd need wider bias strips, but then if the fabric is cool, sounds like a good idea!