I can't think of any natively supported devices that would enable you to grab keyboard focus - the closet I can see would be a mass storage device configured to autorun an application that did the monitoring for you - and I don't know whether it's possible for the Arduino to emulate a mass storage device.
If you want the solution to work without installing any software then the Arduino will need to emulate a device that is supported natively by Windows. There seem to be some conflicting requirements. Push the button again and the Arduino will deactivate. When it recognises a command it sends some predefined message over the BT connection. When activated it grabs keyboard focus and looks for specific keys (or key sequences?) that constitute BT commands.
If I understood you right, you want to be able to push a button attached to the Arduino and have it become activated.