Hello.
1) Please be sure that you activated the Booking Calendar.
2) Please try to deactivate one by one all your active plugins at the WordPress > Plugins menu. Then retest it again.
If its not help, please deactivate your active theme and active the default WordPress theme. And then retest it again. May be there exist some conflict with some active plugin or actual theme and just need to find the reason of that issue.
3) Also please be sure that you are using correct shortcode for the booking form. Please read more how to insert and configure the booking shortcode into the post or page here http://wpbookingcalendar.com/help/inserting-booking-form/
Kind Regards.
