DataGridView ComboBox Databinding for each row

I'm trying to databind my list to my DataGridView's ComboBox column but each row contains different items (default items + another string) which will be eventually stored in a text file. I'm also not sure if I should process the datasource by row since it should allow users to add data or rows to the current list.

I'm getting the following error :

"DataGridViewComboBoxCell value is not valid."

Can you please point-out my mistakes?

Here are my codes :

Main Form :

private void BindItems()
    {
        var _class1 = new Class1;
	colName.DataPropertyName = "Name";
        colList.DataPropertyName = "ColumnList";
        dvMain.DataSource = _class1.myList;
    }

Class1 Class :

public class myData : INotifyPropertyChanged
    {
        public event PropertyChangedEventHandler PropertyChanged;
        public string Name { get; set; }

        private DataGridViewComboBoxColumn _colList;
        public DataGridViewComboBoxColumn ColumnList
        {
            get
            {
                _colList = new DataGridViewComboBoxColumn
                {
                    ValueType = typeof(string),
                    DataSource = _list
                };

                return _colList;
            }
        }

        private IList<string> _list;
        public string List
        {
            set
            {
                _list = new [] { value, "item1", "item2", "item3", "item4" }; 
            }
        }
    }

    public readonly BindingList<myData> myList;

    public Class1()
    {
        myList = new BindingList<myData>();
        var data = new myData
        {
	    Name = "somename",
            List = "test"  // Random string
        };

        myList.Add(data);
    }

I even tried using the IList<string> as the DataPropertyName but it shows the same error.

Thanks in advance.