The mechanics for aerodynamic locomotion in freefall (or zero-g) would drastically differ from what is required on earth. In fact, airflow over a wing in freefall would result in a bird actually moving "up" relative to its body arrangement. That said, a bird would either a) be totally out of control or b) be able to move without shoving off of things in zero-g, depending on whether or not it has adapted to its new environment. My feeling is that most birds would flail around wildly and not really go anywhere; they'd probably just spin out of control or lazily drift in random directions. You might get that one weird bird that "gets it" and learns how to control which direction it drifts. Birds born into zero-g would grow up learning and adapting to their environment and probably have more control.
The above statement is made based on a general knowledge of physics and strong suspicions of how animals would adapt to alien environments. It should not be taken as fact in any way and is easily disputable.