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

I'm glad to see you got it out. "Keep on sucin' 'til you succeeds" was the plan. Their is only a couple of things I would like to add here...
If/when I did chew a stub to hell with vise grips I could still grind that to flush with the surface and use the part, i.e. water pump, as a guide to create a center. That is followed with a #3 center drill, then a 3/16 bit then up the drill size until the very near the minor diameter of bolt threads. Next is a specially ground chisel behind what remains of the bolt to crack and curl it into the middle of the hole. Sometimes the hemostat thing us old hippies call a roach clip would back the remainder out.
So now I must consider that my chisel tool did damage the threads so I'm going to chase the threads. I'll need some chemical as sealant and protectant against water leak and future rust. I'm going to measure the hole depth and grind my replacement bolt so little to no threads protrude deep into the water. Any more length is just a waste of metal.
I've got some white colored product (from Permatex I think). Without looking at its ingredients, I suspect it has some magnesium in it and likely teflon/PTFE too. Many bolts in aircraft assemblies and other applications are coated with this. No seize, no leaks, no rust.
One more statement just for the record... At my 66 years old and lifetime mechanic, I have never owned a left-hand twist drill bit.
I did use a couple that belonged to the company. I recall only two instances when the left-hand twist did grab a very small bolt broken well beneath the surface. The bit grabbed the piece of bolt and backed it out just as its tip broke through the end of the bolt. Those were in Dobby heads built by Yamaha atop waterjet weaving machines.