You want the focus to be as accurate as possible. The most accurate is the very center point. I would set the AF area mode to single point and to center point by pushing the OK button.
I would also increase the shutter speed by increasing the ISO to maybe 400 at least. The D5100 will still give you fairly noiseless photos unless you crop everything to 100%. If the bird starts to fly your 1/200 speed won't cut it.
I don't know the characteristics of your AFS 55-200mm lens at 200mm. You are shooting wide open. I would normally stop down the lens one stop to f8 for greater depth of field. The Pro telephoto lenses are very sharp wide open, the DX zooms maybe not so much.
Given the three areas I mentioned above I frequently use high ISO settings like 1600 and fast shutter speeds on my FX bodies and a little less with DX.
And as mentioned above you want a longer lens, maybe in the 400mm and 500mm focal lengths.