Use a styling hair pick to pick through the bear rug and remove large particles of degree such as cobwebs and dust bunnies. Move the pick through the hair of the bear rug by following the natural lay of the hair, or by brushing from the bear's head to its bottom. Pick through several times to ensure that all large particles are removed.
Prepare a soapy mixture to wipe the rug. Dissolve a mild soap in the form of powder or chips in a container of warm water. Administer only a small amount of soap; lightly soapy water will not require rinsing while overly soapy water will require numerous rinses, which is harmful to the bear rug.
Dip the sponge into the soapy water. Wring the sponge out completely so that the sponge is only damp to the touch and not dripping any water.
Follow the grain of the bear's fur as you wipe the rug with the damp sponge. Rinse and wring out the sponge as the sponge dirties from the dust and dirt on the rug. Mix up a new batch of soapy water if the water becomes too muddy or clouded before you finish wiping the entire rug.
Allow the damp hairs of the bear rug to dry over night and then pick through again to break up any hair that has clumped together during trying. Remember to follow the natural lay of the fur and pick through as many times as necessary to remove clumps and make the rug soft.