Blot as much of the red wine out of the bed sheet as possible with a cotton rag or paper towels.
Hold the area of the sheet where the red wine is located under a faucet. Run cold water through the sheet, flushing out as much of the red wine as possible.
Cover the area with table salt. After the salt turns pink, pour 1 to 2 cups of boiling water over the stain. Refer to the sheet's care label to verify hot water is safe for the fabric, especially for delicate fabrics such as silk or satin. If not, use the warmest water that is safe for your particular sheet to flush the salt and stain out.
Dab dish soap on any remaining stain, and run more cold water through it. You can also blot the stain with white vinegar or 3 percent hydrogen peroxide, but test the product on an inconspicuous spot first. Flush the stain again with cold water.
Bleach the rest of the red wine stain with chlorine bleach if the sheet is bleach-safe. Dilute the bleach first so it is made only of 10 percent bleach and the rest water. Spray it on, let it sit for 15 minutes, and then flush it out with water.