// at some point in my calling code, I will call:
var myDataTable = CreateMyDataTable();
myDataTable.Rows.Add(Guid.NewGuid,tableHeaderId,theName,theValue); // e.g. - need this call for each row to insert

var efConnectionString = ConfigurationManager.ConnectionStrings["MyWebConfigEfConnection"].ConnectionString;
var efConnectionStringBuilder = new EntityConnectionStringBuilder(efConnectionString);
var connectionString = efConnectionStringBuilder.ProviderConnectionString;
BulkInsert(connectionString, myDataTable);

private DataTable CreateMyDataTable()
{
    var myDataTable = new DataTable { TableName = "MyTable"};
// this table has an identity column - don't need to specify that
    myDataTable.Columns.Add("MyTableRecordGuid", typeof(Guid));
    myDataTable.Columns.Add("MyTableHeaderId", typeof(int));
    myDataTable.Columns.Add("ColumnName", typeof(string));
    myDataTable.Columns.Add("ColumnValue", typeof(string));
    return myDataTable;
}

private void BulkInsert(string connectionString, DataTable dataTable)
{
    using (var connection = new SqlConnection(connectionString))
    {
        connection.Open();
        SqlTransaction transaction = null;
        try
        {
            transaction = connection.BeginTransaction();

            using (var sqlBulkCopy = new SqlBulkCopy(connection, SqlBulkCopyOptions.TableLock, transaction))
            {
                sqlBulkCopy.DestinationTableName = dataTable.TableName;
                foreach (DataColumn column in dataTable.Columns) {
                    sqlBulkCopy.ColumnMappings.Add(column.ColumnName, column.ColumnName);
                }

                sqlBulkCopy.WriteToServer(dataTable);
            }
            transaction.Commit();
        }
        catch (Exception)
        {
            transaction?.Rollback();
            throw;
        }
    }
}