Fill Combobox from database

To use the Combobox in the way you intend, you could pass in an object to the cmbTripName.Items.Add method.

That object should have FleetID and FleetName properties:

while (drd.Read())
{
    cmbTripName.Items.Add(new Fleet(drd["FleetID"].ToString(), drd["FleetName"].ToString()));
}
cmbTripName.ValueMember = "FleetId";
cmbTripName.DisplayMember = "FleetName";

The Fleet Class:

class Fleet
{
     public Fleet(string fleetId, string fleetName)
     {
           FleetId = fleetId;
           FleetName = fleetName
     }
     public string FleetId {get;set;}
     public string FleetName {get;set;}
}

Or, You could probably do away with the need for a Fleet class completely by using an anonymous type...

while (drd.Read())
{
    cmbTripName.Items.Add(new {FleetId = drd["FleetID"].ToString(), FleetName = drd["FleetName"].ToString()});
}
cmbTripName.ValueMember = "FleetId";
cmbTripName.DisplayMember = "FleetName";

You will have to completely re-write your code. DisplayMember and ValueMember point to columnNames! Furthermore you should really use a using block - so the connection gets disposed (and closed) after query execution.

Instead of using a dataReader to access the values I choosed a dataTable and bound it as dataSource onto the comboBox.

using (SqlConnection conn = new SqlConnection(@"Data Source=SHARKAWY;Initial Catalog=Booking;Persist Security Info=True;User ID=sa;Password=123456"))
{
    try
    {
        string query = "select FleetName, FleetID from fleets";
        SqlDataAdapter da = new SqlDataAdapter(query, conn);
        conn.Open();
        DataSet ds = new DataSet();
        da.Fill(ds, "Fleet");
        cmbTripName.DisplayMember =  "FleetName";
        cmbTripName.ValueMember = "FleetID";
        cmbTripName.DataSource = ds.Tables["Fleet"];
    }
    catch (Exception ex)
    {
        // write exception info to log or anything else
        MessageBox.Show("Error occured!");
    }               
}

Using a dataTable may be a little bit slower than a dataReader but I do not have to create my own class. If you really have to/want to make use of a DataReader you may choose @Nattrass approach. In any case you should write a using block!

EDIT

If you want to get the current Value of the combobox try this

private void cmbTripName_SelectedIndexChanged(object sender, EventArgs e)
{
    if (cmbTripName.SelectedItem != null)
    {
        DataRowView drv = cmbTripName.SelectedItem as DataRowView;

        Debug.WriteLine("Item: " + drv.Row["FleetName"].ToString());
        Debug.WriteLine("Value: " + drv.Row["FleetID"].ToString());
        Debug.WriteLine("Value: " + cmbTripName.SelectedValue.ToString());
    }
}