How textbox.text is bindable property in XAML

That´s totally ok, DependencyProperties almost always come with such an clr-property wrapper around the actual static representation.

Just have a look at the "propdp" VisualStudio-CodeSnippet, that generates exactly this kind of accessor.

In your case, just look out for a static readonly DependencyProperty:

//
// Summary:
//     Identifies the System.Windows.Controls.TextBox.Text dependency property.
//
// Returns:
//     The identifier for the System.Windows.Controls.TextBox.Text dependency property.
public static readonly DependencyProperty TextProperty

or simply just hit F1 on the member in question, which should take you to the according ;MSDN-Description