Para editar o DataGridview e também salvá-lo em uma tabela de banco de dados usando c#

esquema

create table aster_scripts
(   id int auto_increment primary key,
    i int not null,
    sThing varchar(30) not null
);

insert aster_scripts (i,sThing) values (8,'frog'),(11,'cat');

c#

using System;
using System.Data;
using System.Windows.Forms;
using MySql.Data.MySqlClient;
using System.IO;

namespace WindowsFormsApplication1
{
    public partial class Form2 : Form
    {
        private MySqlDataAdapter mydtadp = new MySqlDataAdapter();
        private BindingSource bindingSource1 = new BindingSource();

        MySqlCommandBuilder cmbl;
        String MyConnection = "SERVER=hostname;" +
                    "DATABASE=dbname;" +
                    "UID=dbuser;" +
                    "PASSWORD=fffff";

        public Form2()
        {
            InitializeComponent();
        }

        private void Form2_Load(object sender, EventArgs e)
        {
            MySqlConnection MyConn = new MySqlConnection(MyConnection);
            MyConn.Open();

            mydtadp.SelectCommand=new MySqlCommand("select * from aster_scripts", MyConn);
            cmbl = new MySqlCommandBuilder(mydtadp);

            DataTable table = new DataTable();
            mydtadp.Fill(table);

            bindingSource1.DataSource = table;
            dataGridView1.DataSource = bindingSource1;
        }

        private void BtnSave_Click(object sender, EventArgs e)
        {
            mydtadp.Update((DataTable)bindingSource1.DataSource);

            MessageBox.Show("SAVED");
        }
    }
}

Chg data hit save Screen Shot

Entradas de banco de dados

mysql> select * from aster_scripts;

+----+----------+--------+
| id | i        | sThing |
+----+----------+--------+
|  1 |        8 | frog   |
|  2 | 11333322 | cat    |
+----+----------+--------+