It is generally permissible for women to use silk bed sheets, while for men, it is debated. The preferred view, according to Imam Abū Hanīfah, permits the use of silk bed sheets and pillowcases. However, natural silk is forbidden for Muslim men to wear, sit, or sleep on. Allah knows best.

Sources:

• IslamQA – Is Silk Haram for Men?
• IslamQA – Sleeping on Silk
• Darulfiqh – Silk Bed Sheets and Pillow Cases