Don't you mean the B.B.C.? Or are we calling it the beebuk now? ;-)
Look at the example of the BBC's style guide. If you're using the BBC guide, then things that are all-cap are said using letters. If we wanted to call it the "beebuk" then it'd be "Bbc" (like "Nato").
We just need all high school teachers to find time between teaching basic literacy to teach kids one style guide for these sorts of things.
The beeb (BBC) works in a similar way. Things that are spelled out are put in all caps ("ACC") and things that are pronounced are put with only a leading capital ("Nato").
Of course, that's just the journalism wonk in me speaking.