This issue can happens at the some servers, depend from the configuration of the MySQL at the version 4.0 - 4.0.1 of Booking calendar.
So for fixing this issue, please open the phpMyAdmin or similar tool for the working with DB
and execute this SQL command:
ALTER TABLE bookingdates DROP INDEX booking_id_dates
or this (depend from the prefix at your DB tables):
ALTER TABLE wp_bookingdates DROP INDEX booking_id_dates
then test it again.