For her second uniform, I would use the single fold bias tape for the wider lines or cut your own white fabric on the bias and sew it down. Then, for the larger white parts, I would use the same white fabric and cut it out with a seam allowance, and then fold under the seam allowance and stitch it down. For the white cross it will be simple. On parts with curves you will have to clip the piece to the edge of the seam allowance and then fold it under so that it curves correctly. Pressing down the seam allowance will help you keep it nice and smooth when sewing also.