What about a Roman shade?

A Roman shade as mentioned by the designer would be beautiful, but the fabric could make or break it. Choose carefully. A shutter would be great here. It could be white wood or vinyl which would pick up the white of the tub. What I love about shutters is they look dressy alone, can be easily cleaned, last a very long time, and have flexibility in the exposure they allow. I believe Hunter Douglas has a shutter with a sandblasted finish that might go with or almost match your tile, however you would have to make sure. It is more costly than plain white but if what they have matches, you've got a winner. If it's not just right though it could be awful and you would want the white.