If you are searching from the google web page there is no easy way to clear the list but I discovered this way. When you click on the empty box as you know all the previous searches are listed put your mouse pointer over the first one so that it turns blue do not click the mouse, then on your keyboard press delete that will delete that entry and the next one on the list will be highlighted so just repeat till all or the ones you want are cleared.
Deleting Cookies/Files and History via Internet Options will not ceal Googlebar history. As stated by watchfull and jazzypop on the left hand side of the toolbar is the words Google with a small black arrow, click on the arrow and select "Clear Search History" or do the same action again and select "Toolbar Options". When the next page opens uncheck "Keep a search history in a drop-down list under the search box" then it wont keep any history at all. The only other option is to download something like Windows Washer and then download the Google Tollbar plugin, this will cost you though.
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