First of all, you should not change any of the original code of your theme or this template page. You should make a child theme and do all the changes there so that when the theme is updated, you don’t lose any of your changes.
What you want to add are custom fields. You can do this yourself if you are comfortable with coding - See the WordPress information here. Or you can use the plugin called Advanced Custom Fields.
Have you tried searching the WordPress.org site for “add more fields to Booking Form”?