Hi Maciej,
In Test Complete 9 and newer you can access Firefox preferences from scripts this way:
Sys.Browser("firefox").Preferences.<PREFERENCE> = <VALUE>
To know what you have to change, just open firefox in "about:config" page and click the button, don't worry about the message. Search for the keyword "search", and you will find all preferences that match that keyword.
Now, pick the preference you want to change (in your case it could be "browser.search.defaultenginename" and set the value you want by replacing it in the previous code:
Sys.Browser("firefox").Preferences.browser.search.defaultenginename = "Bing"
I'm not sure if Internet Explorer and Chrome support something like that, could you tell us please?
Hope it helped!