Where is saving booking data and how to become compliant with GDPR

1. Where all bookings details are saved?

Please note, Booking Calendar plugin saving all booking details at the your WordPress database at your server(s). Its does not transfer your booking details to our servers and does not store such info about booking details at our server(s).
Here is list of all database tables of Booking Calendar that is storing info about the booking details:

    wp_bookingtypes    (available in paid versions)
    wp_booking_coupons (available in  Booking Calendar Business Large or higher version)
    wp_booking_seasons (available in  Booking Calendar Business Medium or higher versions )
    wp_booking_types_meta (available in  Booking Calendar Business Medium or higher versions )

Some info is saving into the wp_options table, but such records relative only to settings, and not the booking details.

2. Additional steps

Its means that your organization need to check and audit your website and booking details, what you store about bookings and apply additional steps to be compliant with GDPR data laws or some other data protection or saving laws. Its your obligatory to be complaint with any law that apply to you depend from your country or saving data.

To be compliant with GDPR data laws you need to check info about this law, because its about what data you are saving during booking process, how your visitor can access this data and how to erase this data, etc...
Check useful link here: http://www.wired.co.uk/article/what-is-gdpr-uk-eu-legislation-compliance-summary-fines-2018
And check this 12 steps prepare guide for General
Data Protection Regulation https://ico.org.uk/media/for-organisations/documents/1624219/preparing-for-the-gdpr-12-steps.pdf
Probably you will be need to check some additional relative info.

The primary details, of what exactly fields about persons you are saving you can check at the Booking > Settings > Form page. Basically its your booking form fields.

3. Adding required checkbox to the booking form, to accept your terms

You can add the "required checkbox" to your booking form at the Booking > Settings > Form page, to accept your terms and conditions and your privacy policy. Its supporting in all versions of Booking Calendar (including Booking Calendar Free version).
Watch this video guide about editing booking form fields in the paid versions of Booking Calendar.

4. List all past bookings and cancel specific bookings (available in paid versions)

In the paid versions of Booking Calendar you can use the ability to list all past bookings of user. So visitor who made the booking, can view all own past bookings (in timeline view, similar to this this example, but relative only to specific visitor).

Also visitor can cancel (move them to trash - its means that you still will require to make complete deleting of them (bookings from trash) at the Booking Listing page, after this request) own pending bookings. Please watch more about this in this video guide.