Dreaming that you are being pursued or attacked by a bear indicates aggression, overwhelming obstacles and competition. You may find yourself in a threatening situation. Alternatively, bears symbolize the cycle of life and death and renewal.  It may signal of period of introspection and thinking. The dream may also be a pun on "bare". Perhaps you need to bare your soul and let everything out into the open.  Dreaming of a polar bear means a reawakening.