The Bluetooth adapter must be 3.0+

The thing is that many 3.0 & 4.0 bluetooth adapters are unsupported in Motioninjoy.

UPDATE - Video guide:
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UPDATED: Text guide:

- First make sure you have ALL old drivers completely REMOVED!
- Insert your Bluetooth Adapter and install it with the original bluetooth software
- After the installation you need to get the MAC address from your bluetooth adapter (Bluetooth settings -> Hardware)
- Install the Sixaxis Pair Tool [ Register or Signin to view external links. ]
- After the installation start the Sixaxis Pair Tool and plugin your PS3 controller (It will install a driver to change the MAC address)
- After the driver installation enter your bluetooth adapter MAC address (with ":") and click UPDATE!
- Close Sixaxis Pair Tool & plug-out the PS3 controller from your PC
- If you have done this then go to your bluetooth suite and add a bluetooth device, make sure you push the PS button when searching! continue without pair codes etc. ... (Don't be irritated by the non stop flashing of the controller)
- Now install Motioninjoy [ Register or Signin to view external links. ]
- Do not start it after installation!
- Re-plugin your PS3 Controller
- Start Motioninjoy, go to device manager and INSTALL ALL
- The bluetooth adapter driver will now also be overwritten but it will work.
- Remove usb cable & click the PS button

If your controller won't connect more to your PC after a restart or relog then you should do this:

- Delete the "MijXinput..." folder in "C:\Windows\System32\DriverStore\FileRepository"
- Uninstall the bluetooth adapter under "Microsoft Common Controller..."
- Install the bluetooth adapter with the original bluetooth driver
- Press the PS Button and the controller should be connected again

If you have followed these steps then you should be able to have a working bluetooth connection with your PS3 controller.
All credit goes to SvenGDK for the tutorial.