Beyond Compare's notification bar doesn't slide, it just pops open, so I can't offer any help on that. The notification bar itself is just a TPanel with a TImage and TLabel for the image/text. It's placed on the main window at design time and it's set to align bottom. Normally it's hidden, and when there's a message to display we set the Visible property to true.
There's different ways to hide the notification, depending on how you want it to behave. In BC we install keyboard and mouse hooks (SetWindowsHookEx with WH_KEYBOARD or WH_MOUSE) and hide it on key up and mouse button events. Alternatively, like Mark said, you could hide it after a delay, add a close button to the side, or just watch for specific events in your app and manually hide it then.