You can add Ecwid search bar using following code:
<div>
<script type="text/javascript" src="http://app.ecwid.com/script.js?STORE_ID" charset="utf-8"></script>
<script type="text/javascript"> xSearchPanel("style="); </script>
</div>
,
where STORE_ID should be changed to the real ID of your store.
Note: Use “ecwid_ProductBrowserURL” parameter (http://kb.ecwid.com/w/page/15853260/ecwid_ProductBrowserURL) to show search results on the page, where Ecwid is installed.