bind the dropdownList as Jason showed you.
Then use another LLBLGenDataSource for the GridView with a SelectParameter tag, that filter upon the selected item/value from the dropdownList.
Example for the second datasource:
<cc1:LLBLGenProDataSource ID="llblgenDS2" runat="server"
CacheLocation="Session" DataContainerType="EntityCollection"
EnablePaging="True"
EntityCollectionTypeName="NWTest.CollectionClasses.OrderCollection, NWTest"
LivePersistence="True">
<SelectParameters>
<asp:ControlParameter ControlID="DropDownList1" Name="CountryName" PropertyName="SelectedValue" Type="String" />
</SelectParameters>
</cc1:LLBLGenProDataSource>