You can configure Booker25 to update the calendar real time. In order to do this, you need to grant users Read access on the Push Topic Standard Object. You can do this on a Profile or Permission set basis. This document explains how to create a Permission Set and assign it to users.
Step-by-step guide
Go to Setup
Search for Permission Sets
Click New
Fill in an appropriate name, e.g. Push Topic Read in the Label field
Press tab to fill the API Name field automatically
Click Save
Navigate to Object Settings
Navigate to Push Topics
Click Edit
Select the Read checkbox
Click Save
Click Manage Assignments
Click Add Assignments
Select the users you want to assign the Permission Set and click Assign
Disabling the Live Update warning toast
Users that do not have PushTopic access will get a warning message when loading the calendar that Live Updates have been disabled. If you have purposefully disabled Push Topic access, you can prevent this warning from being displayed. To do so, go to the Details section of the Settings tab in the Booker25 app, and check the box next to 'Disable live update warning'.
Community user consideration
Salesforce currently does not allow Community users access to the PushTopic object, meaning they will get a warning message when loading the calendar that Live Updates have been disabled. You can prevent this warning from being displayed. To do so, go to the Details section of the Settings tab in the Booker25 app, and check the box next to 'Disable live update warning'.