Hello,
The plugin doesn’t use any shortcodes to output content to pages. Instead, it uses the_content filter to create search result page content, booking object pages content, my account page content etc. and you can see this result on the demo site or screenshots. These pages are created automatically when the plugin is activated, but you can replace them with your own pages in the plugin settings, as described in the documentation. To add a search box to pages and search filters you need to use plugin widgets (add them to the widget areas available in your theme).
In future updates, we plan to add a shortcode to display a list of all booking objects. If you are familiar with PHP you can write your own shortcodes based on function BABE_html::get_search_result(). Or you can order us the customization work.
Hope this helps with your project.