A cover composition that can be applied to a bulk material pile, such as landfill refuse, to protect the pile from wind, precipitation, and access by animals and insects is provided. The cover composition is a mixture of a liquid, typically, water; bentonite clay; and synthetic fibers. The composition may be enhanced by the addition of one or more of the following additives: Portland cement, pregelatinized wheat starch, synthetic polymers, soda ash, and latex paint. Unlike prior art cover compositions, the disclosed composition adheres well to waste material, most notably plastics, whereby the composition is easy to apply and provides a substantially uniform, durable protective cover to landfill refuse piles and other bulk materials. Methods of applying the composition to bulk material piles are also disclosed.