By default the Metro Bing App keeps a history of the things you search, here is how to clear and disable the history feature.
Clear and Disable Your Bing Search History in the Bing Metro App
The first thing you will need to do is switch over to the Start Screen and launch the Bing app.
Now move your mouse to the bottom right-hand corner of the screen to bring up the Charms Bar. Then click on the Settings Charm.
Now head into the Search History settings.
Here you will see a clear all button, click on it to clear your search history. Then go ahead and move the keep search history toggle to the off position to disable the app from keeping your search history in the future.
That’s all there is too it.