Log shipping - Bulk logged recovery mode doesn't log bulk operations, yet it is allowed for Log Shipping config? Why? Log shipping is one of methods for high availability/disaster recovery. It works by transferring the transaction logs from primary to the secondary.

Log shipping needs that the database should be either in full recovery mode or bulk logged recovery mode.

My questions is: Since the Bulk logged recovery mode doesn't log the bulk operations, then why is it allowed in log shipping? Doesn't this mean it violates the principle of high availability/disaster recovery because the secondary database will be missing all the data that was added into primary via bulk operations (as these are not written to the transaction log)?
"Bulk logged recovery mode doesn't log the bulk operations" - it's a wrong message.
Instead of writing information about adding each row to the log file it writes full pages which were affected by a bulk logged operation to the log backup. 

You could read more:
Bulk Changed Map (BCM): The Minimally Logged Advantage