How long does it take before a booking is visible on the display?

Almost instantly.

When a booking is created (via Outlook / Office 365 / Google G Suite) it should be almost instantly visible on the display. If this is not the case there should be informed within Settings > Logs that would explain the cause of the issue.

Additionally, you can check if the booking appears within the personal and room calendar at the same time by checking the room calendar while a booking is created.