I got my HC-05 module to work with the Edison.
For those who don't know what this module is : it's a Bluetooth to serial transceiver module that you can buy for 5$ on ebay. With a Windows or Linux host, you can add the module as a new "virtual serial port" and then open it with any good serial port library or serial terminal program. On the module, you have a RX and TX pins that you can connect to your mcu/device.
I followed the instructions on this site to get the module to work : Bluetooth Serial Communication with HC-05 | MyRaspberryAndMe
At the end of the tutorial, what you get is a new /dev/rfcomm0 device that you can open like any TTY device. It takes no more than 5-10 minutes to setup.