To remove status bar, add showStatusBar="false" in the main Application window.

When we create AIR apps using the Adobe Flash CS4 IDE, there doesn't appear any status bar. But using Flex Builder 3, all the AIR apps will have status bar turned on by default.

<mx:windowedapplication xmlns:mx=""
    backgroundgradientalphas="[1.0, 1.0]"
    backgroundgradientcolors="[#FFFFFF, #000000]"
    height="281" layout="absolute" 

Screen after hiding the status bar