You can do it in two ways:
1. Either you can alter your datasource and rebind the DropDownList.
2. Insert the items in DropDownList in TerxtChanged event of your TextBox(AutoPostBack property should be true for textbox to fire server side event). Try this:
drpList.Items.Insert(0, new ListItem(TextBox1.Text.Trim(), TextBox1.Text.Trim()));
--Amit