When I used WinForms, I would have done this in my bg_DoWork method:
bg_DoWork
status.Invoke(new Action(() => { status.Content = e.ToString(); })); sta
You really should think about using the power of "Data Binding" in WPF.
You should be updating an object in your view model and binding that to your user interface control.
See MVVM Light. Simple and easy to use. Don't code WPF without it.