I have 2 ideas to drill the bearing. Since I don't own a mill, but have a press, I would drill a hole in a clamped piece of aluminium stock the slightly smaller than the ball, take the ball out of the freezer
and drop it in the hole, give the vise a little extra snug and re-chuck a bit for the shaft hole. The other idea is to take the balls to the machine shop here at work and have them chuck it on their rotary table