Q: if the mechanic broke the water pump bolt while trying to remove it- who is responsible to pay for the repair?

A 2011 model year car is "generally" too new to have a bolt so stuck that it is broken on removal. It is possible the mechanic encountered a stuck bolt but simply used the wrong technique to remove it (common mistake). It is possible, but less likely, that the bolt was defective. Either circumstance can be determined, in a forensic examination of sorts, by examining what remains of the bolt, the amount of corrosion, and other standard engineering factors. Again, though, simply due to the newness of the vehicle I would be very suspicious of any "reasons" (or excuses) given to you for a bolt breaking. Unless the car is more than 10 years old, the real "reason" is almost always improper disassembly. Furthermore, charging $1,100 to fix a broken bolt is unheard of, unless you are working on the Space Shuttle, and so obviously there is more to this story. YourMechanic can take over the job, if the car were towed to your residence but then, of course, you would have to disentangle yourself from the present shop. Keep the old broken segment of the bolt and take photographs of the stub that is stuck in the head or block and the area upon removal. If you have further questions or concerns, do not hesitate to re-contact YourMechanic as we are always here to help you.