WPF Application trying to bind my data to a textbox.

Do you want to display the value that you see in the Company_Name column of the first row in the grid in the TextBox called txtCompany?

You could set the Text property of the TextBox in the LoadCompany method like this:

public void LoadCompany(object sender, RoutedEventArgs e)
        {
            DbEstimatorDataContext conn = new DbEstimatorDataContext();
            
            List<Company_Control> Company_Controls = (from s in  conn.Company_Controls
                                                      select s).ToList();
            RadCompany.ItemsSource = Company_Controls;
           
            txtCompany.Text = Company_Controls[0].Company_Name;  
        }

If you want to bind it, you should expose the ItemsSource collection through a property of the DataContext of the TextBlock and specify a valid path to the property you want to bind to:

public partial class wCompany : Window
    {

        public wCompany()
        {
            InitializeComponent();
            this.DataContext = this:
        }
        public void LoadCompany(object sender, RoutedEventArgs e)
        {
            DbEstimatorDataContext conn = new DbEstimatorDataContext();
            
            List<Company_Control> Company_Controls = (from s in  conn.Company_Controls
                                                      select s).ToList();
            RadCompany.ItemsSource = Company_Controls;
           
            var firstRecord = (Company_Controls);
            myGlobals.myCompany_Name = Convert.ToString(firstRecord)
            myGlobals.myCompany_Name = RadCompany.ToString.("Company_Name");
 
     this.Company_Controls = Company_Controls;
        }

 public List<Company_Control> Company_Controls
 {
  get;set;
 }
}

<TextBox x:Name="txtCompany" HorizontalAlignment="Left" Height="23" Margin="77,25,0,0" TextWrapping="Wrap" 
                 Text="{Binding Company_Controls[0].Company_Name}" VerticalAlignment="Top" Width="290"
                 />