How to predict unknown unknowns in machine learning
If you want to predict wether a bird is a bird of one of your two classes or unknown you need three classes: $[bird A, bird B, unknown]$.
For the unknown class you need data from birds which are neither $bird A$ nor $bird B$. You should make sure the number of rows for each of the three classes is roughly the same.
If you don't have data of birds which are neither $bird A$ nor $bird B$ you can use anomaly detection to detect wether a bird is $unknown$ before predicting if it is $class A$ or $class B$.