My bad — I said I was on my iPad so I couldn't verify my reference — the command is — on the Mail menu bar, Mailbox > Synchronize all accounts. That command refreshes the links to your accounts and in IMAP that includes adding any folders that are on the host to those listed on your computer and vice versa. In other words it simply makes certain the account structures on your Mac and the IMAP server match. That does not include any folders On My Mac. The mailbox structure structures for each account on your computer should match the structures on the IMAP servers.

As to the bulk mailbox/folder being an Apple thing, I have several Macs around here, and have access to many more and not one of them has a BULK mailbox associated with any account so it is not standard Mac stuff. Neither is there any Rule condition in Mail that selects on a condition of bulk mail. So I suspect your bulk mailbox/folder is
  1. the product of a third party application that has at one time or another been installed on your Mac and has subsequently been removed or for whatever reason quit working
  2. the result of a Rule you created.

SIDEBAR:
  • I had recently been experimenting with a third party email client and as a result ended up with several unique mailboxes on all of my IMAP accounts. After I gave up on that product and reverted to Mail I had to delete several mailboxes. Fortunately, deleting them on my Mac also deletes them on the various IMAP servers
  • in replying to this thread, I found a couple of Mail rules I forgot I had created and are no longer needed
  • so thanks for prompting me to clean house wink

If we knew what it was we were doing, it wouldn't be called research, would it?

— Albert Einstein