Ok. On the computer I am using, if I delete the URL it goes away but not permanently. If you click on the arrow button at the end of the address bar, the URL reappears! I can only get rid of it if I clear history. So Gents don't rely on the delete function to clear the recorded history in the address bar!
Now to get rid of the history of searches you have done in the google bar, go to TOOLS-INTERNET-CONTENT and disable the AutoComplete function. Seems to work.
Hope this helps.