Firefox’s find bars (yes, there are two of them) are often classified as the good one that is hard to remember, and the not so good one that is easy to remember.
The good one nobody remembers, is hitting the “/” key while browsing a page. If you hit Ctrl+F you get the not so good one that is easy to remember. This is the one that we all use most often. The Hide Find Bar add-on for Firefox merges the greatness of these two searches into one.
How does it do that? It is very simple. It allows you to hide the find bar after a certain interval of inactivity has elapsed. So, when activity in the find bar has been idle for a certain interval it will automatically disappear.
You can try it out for yourself, all you need to do is download the Hide Find Bar extension from the Firefox Add-ons site.