you are trying to assign a
empty datatable
to
bindingsource
.
try like this.
tblnamesbs.DataSource = dt;
tblnamesbs.DataSource = ds.Tables[0];
this.textBox1.DataBindings.Add("Text", this.tblnamesbs, "firstname", true);
this.textBox2.DataBindings.Add("Text", this.tblnamesbs, "lastname", true);