@Html.BeginForm("Search", "Home", FormMethod.Post))
{
    <div class="sub_title_bar">Search</div>
    <table>
        <tr>
            <td>
                @Html.LabelFor(m => m.FirstName)
                @Html.TextBoxFor(m => m.FirstName)
            </td>
            <td>
                @Html.LabelFor(m => m.LastName)
                @Html.TextBoxFor(m => m.LastName)
            </td>
        </tr>
        ... Few more fields.
    </table>
    <button type="submit" class="button">Search</button>
    <button id="btnAdvSearch" type="button" class="button">Advanced Search Filters...</button>
}

<div id="dlgAdvanced" style="display:none; position:page" class="modal-dialog" role="document">
    <div class="modal-content">
        <div class="widget">


            <div class="modal-header widget_collapse_header_bold">
                <div class="sub_title_bar">
                    Advanced Search
                    <button type="button" class="close" data-dismiss="modal" aria-label="Close">
                        <span aria-hidden="true">&times;</span>
                    </button>
                </div>
            </div>

                @Html.LabelFor(m => m.Foo.Bar)
                @Html.TextBoxFor(m => m.Foo.Bar)
                @Html.LabelFor(m => m.Foo.Baz)
                @Html.TextBoxFor(m => m.Foo.Baz)
        </div>
    </div>
</div>

...

<script>
$("#btnAdvSearch").click(function () {
    $('#dlgAdvanced').modal('show');
});
</script>

$("#btnAdvSearch").click(function () {
    $('#dlgAdvanced').appendTo("body").modal('show');
});