You can turn off your Search History to prevent future searches from being saved to your Search History.
But some features, including Google Now, won’t work when your Search History is turned off.
1.Visit your History page.
2.In the top right corner of the page, touch the gear > Settings.
Your Search History will now be turned off for any computers or devices you use with your Google Account.
Note:-Doing so will disable all the search being saved irrespective of the device you use because your settings are saved based on the Google email id you use.
The bar which pop's is something called as auto fill/auto suggest.
Ex:-Your earlier search for Android is stored in your history and later when you simply type Android in the search box it will check for match in the history and display it .(I.e. Although your search is for Android devices and not Android it will display Android in the suggestion bar based on your history)
1.Un-check the search suggestion from
Settings Menu > Privacy > Search and URL Suggestions (un-check this)
2.Clear your browsing history.(auto search suggestion will be displayed based on the history also so you need to clear the history every time you are done with browsing/when ever you open it)
3.Next time when ever you try a search ,The browser will not display the bar which pop's as the auto suggestion is unchecked and browsing history is clear
Note:-If you want to avoid the auto suggestion bar you need to clear your history. If the auto search suggestion bar is seriously annoying for you then you have to trade it with the lost history.
Hope this solves your problem