I might not have explained myself well enough.  Here is some sample code.
My BackgroundWorker is not in the Form

//Controller.cs
public class Controller
{
   private DataAccess _DataAccess;
   public static DataAccess DataAccess
   {
       get
       {
           if (_DataAccess == null)
          {
              _DataAccess = new DataAccess();
           }
           return (_DataAccess);
       }
   }
}

//DataAccess.cs
public class DataAccess
{
   private DataSet _DataSet;

   public DataSet GetMyCustomerData(int ClientID)
   {
       //This is where the database calls occur
       //This is where I was thinking about calling the BackgroundWorker
thread which also removes
       //the need for the UI to know anything about how the data is
retrieved even if it's on it's own Thread
       //I've thought about trying to pass in the Form1 instance and/or a
delegate on the Form1 class to this method
       //also in order to call back to the Form1 class or any Form1 class
for that matter after the process has completed
   }

   //Tried to figure out a way to possibly to make the database calls in
here
   private void BackgroundWorker1_DoWork(object sender, DoWorkEventArgs e)
   {

   }

   //And tried to figure out a way to possibly pass back the DataSet from
the Database call in here
   private void BackgroundWorker1_RunWorkerCompleted(object sender,
RunWorkerCompletedEventArgs e)
   {
       _DataSet = (DataSet)e.Results;
   }
}

//Form1.cs
public class Form1
{
   private button1_Click(object sender, EventArgs e)
   {
        DataSet dsDataSet;
        dsDataSet = Controller.DataAccess.GetMyCustomerData(12345);
   }

   //This was my thought as a possible delegate to get the results from the
Controller.DataAccess method call
   public void GetMyCustomerDataCallback(DataSet dsDataSet)
   {

   }
}