you would need to change the extesnion of the results from .html:
bing_resultspage.html
to .php:
bing_resultspage.php
also, change the action of the form on the serch page to use the new extension:
<form id="BingSearchForm" name="BingSearchForm" method="get" action="bing_resultspage.html">
to:
<form id="BingSearchForm" name="BingSearchForm" method="get" action="bing_resultspage.php">
then you can add the following code to the results page:
You Searched for: <?php echo((isset($_GET["Bing_query"]))?$_GET["Bing_query"]:"") ?>