Can I safely run the microwave for an extended time with just a bowl of water?
Sure you can - heating water is essentially what microwaves are built for. They heat food by heating the water inside. So skip the pizza and use plain old tap water.

You want to take two small precautions, though:  


Use a microwave-safe container, e.g. a heat-proof glass or porcelain bowl.
Take precautions against overheating - a small stone or toothpick should do the trick.