May I ask you why you would want to store booking slots?
I think the right approach is to recalculate available booking slots everytime (via the nettu-scheduler api) a customer asks for it. And then also store the confirmed booking timespan as a calendar event in nettu-scheduler so that the instructor will not be bookable again during that time.
You can have a look at this example: https://github.com/fmeringdal/nettu-scheduler/blob/master/ex...
Well, I was thinking of saving the booking slots presented to the customers for data purposes. Also, I was thinking that it might help to store the presented slots in case someone else books it before the person decides to reserve. This way eliminating the option in realtime might be easier and without having to recalculate all the remaining available slots again? But maybe there is a better solution to this....