While binding dropdown list control you need to set three properties.
Say "ddlBook" is dropdown control. It should be as shown below.
ddlBook.DataSource = dictCountries;
ddlBook.DataTextField = "Text";
ddlBook.DataValueField = "Value";
ddlBook.DataBind();
If you set the text and value fields. You will be able to access the value with below code:
string selectedVal = ddlBook.SelectedValue.ToString();
If you are able to find the instance of the drop down inside the grid row, then the above code works.