Sounds like the bolt is broken off with just the threaded part still in the hole but without any of the shank exposed, otherwise he'd just use vice grips to get it out.
What's needed is a bolt extraction kit, commonly referred to As an easy-out kit. The thing about these is that you need to drill into the bolt and access is typically not sufficient where a water pump is. Sometimes you have to take the piece that the bolt is stuck in to gain enough access.
Does the water pump on a BMW bolt onto a timing cover? If you can't access the bolts to use an easy out, you'll have to remove the timing cover to gain access. Go to sears to see what an easy out kit is and how it works then once you know how to use it see if you have clearance to do it on the car and if not then gain clearance by removing surrounding parts or removing the timing cover with the stuck bolts. Then find a place that will rent you the easy out kit. Maybe centerville rents or a cresco or maybe even a kragen auto if they still rent tools. Or ask around to see if someone you know has one. Then when the bolts are out, run a tap through the holes to clean up the threads before installing new bolts.
BTW, how did this happen? Did you over torque them, or did this happen while removing the bolts? Reason I want to know is this has happened to me before on a different car and at a different place while removing bolts after a short drive that I had just torqued to spec before the drive. The only reason I could figure why was because it was a steel bolt in aluminum and they expanded differently from the heat of the engine, making the threads slightly off from when they were cold.
J
