Maybe you could uncheck the box always show timeslots in business timezone?
Have a look at the following answer already logged:
https://answers.microsoft.com/en-us/msoffice/forum/all/microsoft-bookings-time-zones/814553d0-a1d5-41d2-94da-58097c37d07b
Regarding your concern, I've done my test. According to my test result, what time slot people in a different time zone will see relies on the time zone settings on your Booking Page. If you select Always show time slots in business time zone, the time slot in your published page will conform to your setting in the Current time zone in your Booking Page. If you uncheck Always show time slots in business time zone, the time slot will conform to the viewer's local time.
Take my test as an example. At first, in the Booking Page, I specified the Current time zone to be (UTC) Coordinated Universal Time and selected Always show time slots in business time zone. Also, I set the Time increments to be 5 minutes and Minimum lead time to be 24 hours. Since the time I Save and publish my setting on Booking Page was around UTC 8:05 am August 28, plus I set the General availability to be 24/7 available, so the earliest available time for a new booking should be my publishing time plus with 24 hours and 5 minutes which is UTC 8:10 am August 29.