Well, the windows, app bars and such are controlled by a window manager. There are a lot of them out there for linux though Gnome and KDE seem to be the most common. KDE is actually based off of the Qt libraries.
Qt is developed and maintained as a cross platform graphics library so it is a good place to start. You can get some information about it
here. It can most likely be used for free but it all depends on what you plan to do with the app bar. (Read the liscense just in case)
Gnome has it's own set of graphics libraries that should be able to be run on any linux computer (though this would require installing the entire window manager). I truly think that if you want to be able to use it on any linux distribution that Qt is your best bet.
Edward
Note: This question would probably have been better to ask on the Linux forum because of it's linux specific nature and the fact it has more to do with linux graphics then with actual c/c++ programming.