By default in Firefox you can type one or more keywords in the address bar. Firefox recognizes that it is not an URL and uses the I’m Lucky search with Google for Firefox version 2 and above. Here is how you can change it to Bing.
Type about:config in the address bar and press Enter
Type keyword.URL in filter and double-click on the displayed line. You will note that the default value is something like: http://www.google.com/search?ie=UTF-8&oe=UTF-8&sourceid=navclient&gfns=1&q=
Change it to the following string: http://www.bing.com/search?q=
Hit OK and close the browser tab
Now you are set to use Bing to search using the address bar.