How much bandwith does WoW use?

WoW uses very low bandwidth; it has a highly optimized and efficient system that generates small packets of information to make it usable on a variety of different connections. This also makes latency much more important than bandwidth when playing WoW.
It’s hard to say an exact number because that depends on many factors, like # of actions from other players, number of adds/bosses, pets, etc…

If you want to be sure about the values you can always check the current usage at any given time without using any 3rd party software, at least you can if you’re running Windows 7, all you have to do is go to the Task Manager-> Click on the Performance Tab -> Resource Monitor -> Network Tab , and there you should be able to see the bandwidth usage of every active application, including WoW.