We recently discovered these 100% natural linen sheets by Area Simone. Linen, which comes from the flax plant, is an optimal material for making sheets. Like hemp, linen does not require pesticides to grow. By contrast, 25% of all pesticides used in the world are sprayed on cotton. Linen is also 2 to 3 times stronger than cotton, has no lint or piling tendencies, and dries more quickly. These sheets are priced from $94 to $315, and they are available from Design Public. They also sell matching pillow cases and duvet covers.
Amazon has a wide range of natural linen sheets.