If my white fabric is too thin I will double it up and do two layers but that is rarely necessary. I have found Robert Kaufman Kona solids and Moda Bella solids plenty thick to hide travelling lines on hand embroidery. When I knot off I weave the tail into previous stitches before knotting to hide those. Once layered up with batting and quilted I have had no issues. Here is an example of a quilt I recently finished that had sashiko hand embroidery on white with dark blue thread. This is one layer and none is showing through.