the search form will be created on the search page as:
<form id="BingSearchForm" name="BingSearchForm" method="get" action="bing_resultspage.html">
<label for="Bing_query">Search for: </label>
<input type="text" name="Bing_query" id="Bing_query" value="">
<input type="submit" name="button" id="button" value="Search">
</form>
you can put that in to a template as long as the action:
action="bing_resultspage.html"
point to the results page.