Arduino Bluetooth Piconet - Feasibility and Suggestions

As Nick says, Bluetooth Classic is not the best solution for this. It could be done with BLE but would need true BLE not the cheap UART modules like the HM-10.

Have a look at MQTT and the ESP8266. There is already a lot done for this and you will probably be able to find ready made solutions. The only down side is that MQTT requires a server but this can be something like a pi rather than a full desktop.