Your lens will be sharpest at f8 Dxomark lens report. To hand hold at 250mm, the rule of thumb is 1/250th of a second (and preferably faster). I know you have IS but if the bird is moving even a little you still want a fast shutter speed to freeze the motion.
For the sharpest image, if you don't have bright enough light for 1/250th at f8 you will need to boost your ISO rather than using f5.6 or a slower shutter speed.
Try ISO 400 or 800 if your lighting is overcast.