I changed my default search provider this way.

1. Open the Web Browser.
2. Type "about:config" in the address bar & hit enter.
3. You'll get a warning(If you do this in desktop Firefox, you get the same warning). Accept & proceed.
4. You'll get a huge list of entries.
5. In the filter area, type "keyword.URL" or just scroll down to it in the table
6. Highlight the above entry and then press enter(from the keyboard)
7. IMPORTANT: You may want to save the current value somewhere if you want to get back to it later.
8. Change the value from original Google to "http://www.bing.com/search?q="
9. Save it. Close the about:config window.
10. Now whenever you type words in the address bar to search and hit enter, it'll go through Bing. But the auto suggest feature will also show "search with Google". Both will work which is the best part.
11: Enjoy