(this is for my first post translated in English, I'm already sorry for all the mistakes you would find in it)
I'm currently developing a new app, HFR RT, in which I wanted to display a Minimized state of my AppBar, à la Windows Phone.
Note that the new Mail and Calendar apps included in Windows 8.1 have the same behaviour. In my opinion, we should find this behaviour in every built-in apps and Microsoft should provide an API to do that.
Anyway, here's this little piece of XAML, that you can put into a UserControl or directly in your Page.
Don't forget to name your page, if not the Binding will not work (here the page is named MyPage).
Then, you just have to add this line in the Tapped event:
BottomAppBar.IsOpen = true;
That's it !