The three criteria for a USB stick to appear in the dropdown picklist are that the device needs to be...
That third one is important. Also, we've noticed that sometimes the OS doesn't see specific USB sticks as removable. There's an easy way to check both of these. Right-click or control-click on the USB stick on your desktop and select "Get info." Is the icon orange or white? It should be white to indicate it's removable. And you can check to see if it's writable at the bottom of the info window.