It depends!!
Normally, continuous and centre focus point, but it depends on a number of factors. Namely, the shot I'm after (i.e. the ultimate framing), the flight direction of the subject, and how large the bird is in the frame (and importantly how large it will be in the frame for the "final shot"). This last point is especially important. You're typically going to track a bird as it moves closer to you - so it's getting larger in the frame. At what point is the best shot and where will the bird's eye need to be for the best shot. For distant subjects that don't fill the frame this is of less importance (and you'll likely be cropping), but for close subjects, especially those with long tails, then centre focus point could have me on the body rather than the head.
For example, consider a bird flying left to right with a long tail (think something like a macaw) - centre focus point would have me wasting a significant amount of the frame in front of the bird leaving a lot of unwanted negative space (noting that you'll need some space in front of the bird to allow the subject "space" in the frame) and in the same instance I'd also run the risk of cropping off the tail. In such an instance I'd be right of centre.
A good tell-tale sign that a sub-optimal focus point is used is look at the framing before cropping. If there's lots of wasted space in-front of the bird, and you're cropping it away, then in such instances the centre-point is not the most optimal focus point to be using.
Of course, there are many occasions when you won't have time to adjust the set-up, and you'll have the option to achieve the best framing by adjustments in post production. But in some instances birds will fly in a predictable direction (for example, larger birds typically turn into wind as they land).
Martin