Reserve Calendar Time for Bookings

How do you block space out on your personal calendar such that it's only available to Microsoft bookings, and shows busy to others in your organization?

I've created a personal bookings page with custom timeslots--that's working just fine. The problem is that people in my org who can see my calendar are sending calendar invites for those same timeslots, making them no longer available to the bookings page. If I add my own events to my personal calendar to mark time as busy, those slots also disappear from the bookings page. 

How can I adjust things such as to reserve time exclusively for Microsoft bookings and no other users at my org?