Right click on the bouncing icon and go to 'Force Quit'.
Done and dusted.
BUT, if it doesn't go away within 10 seconds, then you may need to restart your computer. And if entourage does this everytime you open it up, then i'm afraid you might have a problem with Entourage. I'll leave it to someone who is more accomplished at Entourage to tell you how to reset the program without removing your emails etc.
Is it just bouncing when you launch Entourage (which is normal for any application) or are you complaining about the bouncing when receiving new mail messages (this can be turned off)?
You can post another message to this thread with your answer or for faster response send me a private message. I have been working with Entourage for many years.