To properly dispose of used black fiberglass tissue, follow these steps: First, ensure that the tissue is dry to prevent mold growth. Place it in a sealed, heavy-duty plastic bag to contain any fibers. Avoid puncturing the bag, as fiberglass can be harmful if inhaled. Check local regulations, as some areas have specific disposal guidelines for hazardous waste. If your local waste management facility accepts hazardous waste, take the bag there for proper disposal. If not, contact a professional hazardous waste disposal service. Always wear protective gear, such as gloves and a mask, when handling fiberglass to minimize skin and respiratory exposure.