I've successfully built the connection between Android phone and Intel Edison, by following the article: https://software.intel.com/en-us/blogs/2015/05/19/communicate-to-arduino-code-with-your-android-phon... communication to Arduino code with your android phone by Bluetooth serial port profile on Intel Edison and the python bluetooth service files provided. I was using Android app to control the Edison by sending text messages (messages then handled by an Arduino program).
Now, I'm trying to replace the Android phone with my PC. Could you give me any clue about achieving so, i.e., how to send messages from my PC and receive them at the Edison end, preferably using BT SPP?
For all Bluetooth related I would suggest you to check the Bluetooth Guide for Edison, http://download.intel.com/support/edison/sb/edisonbluetooth_331704004.pdf http://download.intel.com/support/edison/sb/edisonbluetooth_331704004.pdf.
Regarding your question, you could apply the same process that you used to connect your Edison to your Android phone, at least from the Edison side you should use the same commands to pair, discover and connect to your PC. Now, instead of using Bluetooth SPP Pro it would be necessary to found another way/software to handle Bluetooth devices (probably Putty would be the easiest way).
If you're willing to try some other profiles I would suggest you to check the PAN profile, on page 39 of the Bluetooth Guide.