Set your Homepage to Bing.
http://www.bing.com/

http://support.mozilla.com/en-US/kb/How+to+set+the+home+page

Easy when you know how.

I don't want to change my homepage. I just want to have the choice in the search box top right of having Bing in addition to Google and Yahoo.

Install the Bing search engine: http://mycroft.mozdev.org/search-engines.html?name=bing

I try to install and it says Firefox is not supported. I have os 10.5x but only a powerpc machine. Does it require intel? If so they should say!

Going to http://www.discoverbing.com seemed to do the trick for me. I clicked the big orange button that said 'Make Bing your default search'. A dialog came up asking if I wanted to install it in my search box. One more click--and I was done. Hope this helps.

After some searching, here's how:

Make Bing Your Search Engine

   Click on the search engine icon (the little down arrow) in the search box in the upper right corner of  your browser.
   Select Bing.
   Start searching!

I feel sorry for people who didn't have the patience to scroll down for the ACTUAL correct answer: Make Bing Your Search Engine Here.