Probably, you have inserted the shortcode for only "availability calendar" [bookingcalendar type=1] instead of shortcode for booking form [booking type=1].
Please note, this shortcode [bookingcalendar type=1] is only for showing availability calendar without form, where you can not select the dates. Booking form shortcode [booking type=1] already contain calendar and there you can select dates and submit the booking.
How to fix it?
Please open that page for editing and then remove exist shortcode.
After this switch from the "Visual" view mode to "Text" view mode your content editor. And then reinsert the Booking Calendar shortcode. You need to insert shortcode like this: