in the centre of the Earth, all mass is divided equally around you. This means that the sum of all individual gravity vectors is zero. So there is no up or down, just no gravity and the ball bearing would behave exactly as in a spaceship. If you move it off centre a little but, the influence is minimum, changing the total sum only with an infinitemisal small amount.
The pressure in the centre of the Earth is tremendous of course, so it would be a bit hard to dig that hole and get a bearing inside.