All animals in dreams represent an emotional aspect of your own nature giving you the ability to feel or act in a particular manner. The bear is often used to represent a feeling of having a lot to bear, a lot to put up with or tolerate.
As you are being chased by the bear, it would suggest this feeling of having a lot to bear is one that you are unable to shake off or lose.
Here you are running away from this animal because it is perceived as a dangerous one. In other words, where you are living with the feeling of having to put up with a lot, your own emotional nature is not working in your favour or best interests, but rather as a great danger to you as a rational human. The animals are instinctive feelings and irrational ones. A grizzly bear image may simply be emphasizing the dangerous aspect of this irrational feeling. [Is your feeling of having a lot to bear a response to logical thinking or emotional thinking?]
If you dream constantly about bears, this feeling of having a lot to bear is one that you may need to examine more closely.