The BCV copy is performed by the Symmetrix, not the host.
To copy your standard device, you use the symmir ESTABLISH command (Solutions Enabler or ECC). While the relationship between Std & BCV is establish, your 'mirror server' will not have access to the device - will be 'Not Ready'
To use the BCV you need to use the symmir SPLIT command.Once split, the device will become rw enabled and the 'mirror server' will have access (may have to rescan the host)
Whether your 'Mirror Server' is up or down is irrelevant to the synchronising process. If not using the 'Mirror Server' you can leave the pair Established, and only Split when needed - the longer you have the pair Split, the further behind the BCV will be from the production disk.