There is actually a simple search form shortcode included in Total which you can use to place a simple search form anywhere on the site (there is also a search form Visual Composer module with many options). If you want to add a search to your Top Bar you can do so via the shortcode if you aren’t displaying VC content in this area.
Simply use the shortcode to display the default site search form:
This will pull the code from the searchform.php file so there aren’t any parameters available for the shortcode.
Below is an example of the shortcode in action: