Hi micah,

Check this example. Now please take its reference and correct your code.

HTML

<asp:DropDownList ID="ddlCountries" runat="server" multiple="multiple" 
    CssClass="multiselect" data-placeholder="Select Country">
    <asp:ListItem Text="Argentina" Value="Argentina"></asp:ListItem>
    <asp:ListItem Text="Austria" Value="Austria"></asp:ListItem>
    <asp:ListItem Text="Belgium" Value="Belgium"></asp:ListItem>
    <asp:ListItem Text="Brazil" Value="Brazil"></asp:ListItem>
    <asp:ListItem Text="Canada" Value="Canada"></asp:ListItem>
</asp:DropDownList>
<script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
<link rel="stylesheet" type="text/css" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.0.3/css/bootstrap.min.css" />
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.0.3/js/bootstrap.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/bootstrap-multiselect/0.9.13/js/bootstrap-multiselect.js"></script>
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/bootstrap-multiselect/0.9.13/css/bootstrap-multiselect.css">
<script type="text/javascript">
    $(function () {
        $('[id*=ddlCountries]').multiselect({
            includeSelectAllOption: true
            //,nonSelectedText: 'Select Country'
        });
    });
</script>

Screenshot