Just saw this over on The Road to Know Where, and is really quite nice… You can run through a quick wizard over on the Bing Site Owner site, and it will generate some HTML that you can past on your site to add a Bing Search Box that will search both the Internet and your site.
The search 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.
Basic Search Box – Displays results on the Bing website. Searches a single site that you specify, or the entire Web.
Advanced Search Box – Displays results on your site. Searches multiple sites you specify, the entire Web, or applies a Bing Macro.
Get it here: http://www.bing.com/siteowner/