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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.
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.