Hello,
I’ve checked the page where you placed the Booking Form and it seems that the Ajax request was not properly executed they gave the 502 – Bad Gateway error. please note 502 – bad gateway error is not from the BookingPress side it comes from the server side. I would recommend you please check it with your hosting provider with the configuration and ask them to check for the logs about what caused the issue for the service being unavailable as this error does not belong to the BookingPress but the server configuration.
Also, herewith, I’m attaching a screenshot for your reference.
https://prnt.sc/5nyYOYUgWk_d
Thanks