Change the following to
Binding binding = new Binding("Property");
binding.Mode = BindingMode.TwoWay;
binding.Source = testClass;
this.txtBox.SetBinding(TextBox.TextProperty,binding);
or
Binding binding = new Binding();
binding.Mode = BindingMode.TwoWay;
binding.Source = testClass.Property;
this.txtBox.SetBinding(TextBox.TextProperty,binding);
When you specify Path on the Binding class contructor, the Source property should be the object.