Broke my water pump bolt. Now what? (Update - broken bolt is out)

Wow. I've drilled out dozens of broken bolts in my life. Is it good to be perfectly centered? Yes. Will the sky fall if you aren't? No. You have to keep the brain engaged when you do this. You don't try to drill out a 3/8 bolt with a 3/8 bit for a start. Start small and work your way up until you hit the minor diameter of the bolt, wherever that occurs, and collapse it. Frankly, I've had more trouble keeping the bit straight when drilling out a bolt than finding the center.