Try this,
button click event
protected void btnAddItem_Click(object sender, EventArgs e)
{
session["cbItem"]= textBox1.Text;
Additem();
}
On page load
protected void Page_Load(object sender, EventArgs e)
{
Additem();
}
public void AddItem()
{
ComboboxItem item = new ComboboxItem();
item.Text = session["cbItem"].Tostring();
item.Value = session["cbItem"].Tostring();
comboBox1.Items.Add(item);
}