If you want to make it as the default search engine then click on the "customise Google chrome" option and select "options". There go to the tab, "basics". Under that you wiil find Google as the default search engine. Click on "Manage" .Change it to bing.com by selecting the bing.com in the "other search engines list". This is possible only if you had pressed "tab" in the address bar as I had told previously. If you have not done that either do it or copy the following URL and place it in the URL box that is to be filled while adding the search engine.
URL: http://www.bing.com/search?q=%s&go=&form=QBLH&filt=all
So, after pasting this click on add button and you will get the Bing search engine. Click on "Make Default" to make it default.
Here u\is a way to add Bing search in Opera 10 beta