Is there any story to the bird?

Half-Life Wiki has an explanation for the bird in Portal 2:

The bird, a crow based on the caw she makes, is a minor antagonist in Portal 2 to the AIs Wheatley and GLaDOS. The bird attacks Wheatley after he used her eggs to break a door, and kidnapped GLaDOS while she was a potato. After this GLaDOS becomes incredibly afraid of birds, telling Chell to kill it. At the end of the DLC Peer Review co-op stage, the bird is chased out and locked out of Aperture by P-Body and ATLAS, though GLaDOS told them to abort the mission and run, because she had no plan. The bird's eggs are hatched by GLaDOS after this, with GLaDOS planning to raise them into little killing machines.