The woolly bear is a common and well-known caterpillar. Though most people have one kind of woolly bear in mind, there are 8 or more species in the U.S. that could legitimately be called woolly bears because of the dense, bristly hair that covers their bodies.he best-known woolly bear is called the banded woolly bear. It is black at both ends and reddish-brown in the middle. The adult is called the Isabella moth. The banded woolly bear is found throughout the U.S., Mexico and southern Canada but not the rest of the world.