It does use bandwidth on a Wi-Fi network, although not all too extreme of amounts unless you constantly ask it questions.
It does also use data on a cellular plan, although again, not a lot of data. Data usage will depend upon how often you ask Alexa questions and/or if your device is connected to wi-fi. If your phone is connected to wi-fi while using Alexa, you will use no data from most cellular carrier's plans. If you are not connected to wi-fi, data usage is minimal and depends upon how often you ask it to do things. Amazon Echo uses data since it is connected to your phone through the Alexa app.