Unscheduled reservation

Hello.
It’s depend from what functionality do you need from the form in your example.
If it’s just contact form for sending emails, so then you can use any contact form plugin, like “Contact form 7”.

If you need to have ability to cancel the previously created bookings by visitor who submit such booking, so then such functionality available in the paid versions of Booking Calendar. Please check this FAQ instruction how to configure ability to edit or cancel own booking(s) of visitor, who made these booking(s): https://wpbookingcalendar.com/faq/configure-editing-cancel-payment-bookings-for-visitors/

If you need to show for users all past bookings of this user, then check here: https://wpbookingcalendar.com/help/user-bookings-listing-video-tutorial/

Kind Regards.