Tap the URL field and start typing what you want to search for - as you start typing the screen should change to a search screen with an 'on this page' option on it, which if you select will take you back to your site with the search options at the bottom of it
I don't understand your answer! I tried to do what you suggested but it just takes me away from the page I am on and there is no "search screen"! Any chance you could provide some screen shots? I find the new safari very awkward and hard to understand.