It may also have to do with diffraction of light.
Snowflakes, if you looks at them individually are clear transparent, or rather translucent, so why does it look white? Because the light goes in and through them ,and gets bounced around and basically comes back out. The same happens with your shave suds. The individual bubbles are clear and translucent, so the light goes in, bounces around and comes back out.
Try replacing the bulbs in your bathroom with black lights, put on some Pink Floyd and then check out what your lather looks like!
