I have found that if you use a light fusible stablizer on the fabrics it works well. You need to wash the silk but before you do, you need to surge or zig zag the edges to keep them from fraying. This not only shrinks the fabric but will take care of the bleeding of the dye. Yes you can wash silk, it is a natural fiber.
Be sure to fuse after the washing. You may iron the silk wet. I hope this helps. RuthAnn