Sure, somethink like

<asp:BoundColumn DataField="MyField" >
   <ItemStyle CssClass="Invisible"></ItemStyle>
   <HeaderStyle CssClass="Invisible"></HeaderStyle>
</asp:BoundColumn>

and

.Invisible{display:none}

somewhere in styles.

I figured it out.  THANKS to everyone for your help!  I explained what
I did to solve the problem below in case anyone else is interested.

Instead of attempting to retrieve Invisible column data (which doesn't
work upon PostBack) I removed the columns from the DataView and I used
the DataKeys property instead:
gvParts.DataKeys(e.RowIndex).Item("StretchOut")
gvParts.DataKeys(e.RowIndex).Item("NumBends")
gvParts.DataKeys(e.RowIndex).Item("SN")

To retrieve a template field in my GridView control I used the
FindControl method:
Dim txtLengthBox As TextBox =
gvParts.Rows(e.RowIndex).Cells(7).FindControl("txtLength")

The Entire Code is here:
   Protected Sub gvParts_RowUpdating(ByVal sender As Object, ByVal e
As System.Web.UI.WebControls.GridViewUpdateEventArgs) Handles
gvParts.RowUpdating
       Dim txtLengthBox As TextBox =
gvParts.Rows(e.RowIndex).Cells(7).FindControl("txtLength")
       Dim CusVal As CustomValidator =
gvParts.Rows(e.RowIndex).Cells(7).FindControl("cvLength")
       If Trim(txtLengthBox.Text) <> "120" And
gvParts.DataKeys(e.RowIndex).Item("StretchOut") = "48" And
gvParts.DataKeys(e.RowIndex).Item("NumBends") = "0" Then
           'Do not allow the user to change the length of a sheet of
material.  Sheets are always 120 inches in length.
           CusVal.IsValid = False
           txtLengthBox.Text = e.OldValues("Length")
           e.NewValues("Length") = e.OldValues("Length")
       Else
       End If
   End Sub