lucy24 - 5:22 am on Oct 21, 2012 (gmt 0)
Well, you could swipe the code this site uses, substituting your own site name and, ahem, inserting quotation marks and adjusting capitalization as appropriate ;) Not technically a site search, but your users may not care.
<form action=http://www.bing.com/results.aspx target=_blank><input TYPE=text name="q" size="50"> <input type=submit value="Bing!"><input type=hidden name=q1 value=site:example.com></form>
I assume you found the pages about the Bing Search API, made for www sites using-- it says here [datamarket.azure.com]-- XML or JSON. It's all so much Hungarian to me.