Why do the docs not mention adding "bridge" as its own tagged interface when doing a VLAN trunk?

No. You only need to add the bridge as a tagged member for traffic which interacts with services provided by the CPU, e.g. a router-on-as-stick setup with multiple VLANs. See http://forum.mikrotik.com/t/routeros-bridge-mysteries-explained/147832/1 for more information.