Currently there is no way to disable either Wifi or Bluetooth using Apple Configurator profiles. Configurator has gotten much better over the past few years limiting various activities in academic environments, but it does not allow restrictions on a number of things that they deem important, like network & device connectivity.
Other activities, like installed new iOS updates, are also cannot be locked down. This bit us hard when 8.1 was introduced, as a number of our 1:1 students with managed iPads updated to 8.1 Several of the apps they need for their schoolwork needed updates as well and crashed, but because we restrict the App Store, we had to do a mass update with Configurator over the course of a day.