Hi Ivan,
Greetings from Syncfusion Support.
We can block time slots and allow booking appointments by using allowAdding option in eventSettings. We have shared a sample for your reference which can be viewed from the following link.
<ScheduleComponent
height="650px"
ref={schedule => (this.scheduleObj = schedule)}
selectedDate={new Date(2019, 0, 10)}
eventSettings={{ dataSource: this.data, allowAdding: false }}
>
Please try the above solution and let us know if this meets your requirement.
Regards,
Nevitha