How to Hide Android Screen Keyboard When paired with Bluetooth Keyboard
* Null Keyboard prevent on-screen keyboard from popping up all the time. After you have installed it on your device, you need to activate it. Go to Settings > Language & Keyboard, and check the box with "Null Keyboard". When you are edit email or write message with friend, just change the input method to it. To get it working better, you can use Tasker app to automatically toggle input method.
* AnySoftKeyboard detects a key press event from an external keyboard and then automatically hide the on-screen one. Once it is installed, go to Settings > Languages, and tick AnySoftKeyboard. Then tap on its settings button and check "Hide keyboard on physical key" box. This is the best way if you often need to switch between two keyboard.