Bluetooth has been an ongoing topic in a few forum threads.
Pairing Intel Galileo w/Device via Bluetooth
Re: Bluetooth and BlueZ and Servers, Oh My!
Re: Does the Galileo support bluetooth via the n135 card
To get Bluetooth to work for Arduino, you first need to get it to work in Linux. I am not sure if anyone has been successful with that.
The next step is to get Arduino to talk to the Bluetooth. I am pretty sure no one has been able to do this (but honestly, I cannot keep up with everything posted in this forum. :-) )
There are more details in the other Bluetooth threads. I think it can be done, but will require some porting of the Arduino libraries.