DC coupling has nothing to do with an output stage being bridged. You should always shut down fully when attaching cables. Shorting cables is the worst thing you can do to a live solid state amp. Although I wasn't aware the XA25 was a bridged design.
When an amp is bridged both binding posts carry signal (hot), neither is grounded. Shorting to ground will blow the amp. This may be a problem with some subwoofers if one speaker level is grounded.