Is it possible for search terms to appear in the search bar of an iPad just from going to a "bad" website? I was told that some search terms appeared in the search bar of an iPad because that person had gone to a "bad" website and the terms must have come from that visit.
The search bar should only offer suggestions based on your website history, your bookmarks, or searches that you have typed in and hit enter for.

It won't scour the pages you have been to, looking for related terms.