TheKitty:
Correct, no one has ported the AVR specific software serial library(ies) to the Due.
So sad that its not :(.
But I tried what you are talking about once before, I'm pretty new to the Arduino especially the Due, I just tested the bluetooth using the blueterm app on my android phone.
Similar to what TheKitty said though, I had to connect the bluetooth module (I was using the xbee shield) to I think pins 17 and 18 or RX and TX because of this problem. I'm guessing you might be able to do something similar (although probably with the actual correct pins). And as he said I just had to change the code from software ones to serial calls. I didn't have to change anything else hardware wise (although since I was using the shield I had to change this little plastic thing to make sure it output to the correct place)