Question

How do I manage the booking options for my resource mailbox in Office 365?

Overview

Users need an O365 mailbox to create and log into Bookings. For simply interacting with Bookings (non editing), users do not need an O365 mailbox. 
If you or your users need an O365 mailbox, email ithelp@ucdavis.edu for assistance.  

Answer

If you want more detailed resource booking options, you must give yourself full mailbox permissions on that resource by clicking on the mailbox delegation tab on the resource properties and then adding an account to the full access list. 

When you log into the Office 365 ECP, you can locate the resource mailbox by going to recipients and then clicking on Resources. View it's settings and see the Booking delegates and Booking options tabs on the left. This is where the In and Out of Policy options from Exchange On-Premise are located.

If you want more detailed resource booking options, you must give yourself full mailbox permissions on that resource by clicking on the mailbox delegation tab on the resource properties and then adding an account to the full access list.  Once added, use that account to log into 365.ucdavis.edu.  Click on your picture in the upper right of the screen and select open another mailbox.  Enter the name of the resource.  Once that mailbox opens (it could take a bit for the permissions to replicate), click on the gear in the upper right and select options.  Then Click on Settings on the left.  Under the resource tab, you will have more options such as who it will accept messages from.

Be sure to go back and remove your full mailbox  permissions when done.