Agreed. Start in the center of the remainder so that as you step up bits it'll try to reach the first hole and the edge of the broken bolt about the same time.
Is that a damn easy out broke off in that hole?
As the hole you're drilling gets larger, you'll be able to see threads in the side of the hole. Stop drilling at that point. You don't want a big groove cut into those threads. You want as much of those threads remaining as possible.
This needs to be closer to a gyno exam, and less prom night in the back seat.
