The Bing Developer team recently announced that the "Bing Box" functionality on bing.com/siteowner will be discontinued on April 4, 2011. From 4th April 2011, Websites attempting to use search box will be redirected to a 404 page. That means websites interested in receiving web or site search results from Bing, need to be switch to Bing API.
Here what they say:
We have decided to take this step for two reasons.
First, the tool has not been getting a lot of use and while we have some very loyal customers on it, we believe we can provide you better alternatives in the future as we free up resources.
Second, the functionality available through bing.com/siteowner can be replicated with the Bing search API and so it feels a bit redundant.
The Bing box powered by Bing provides a fast, customizable search solution for your website or blog. Visitors to your site can search the entire Web, just your site, or any sites that you choose.