I don't know if its so much break in as it is warm up. Any digital component I've had - CDP or DAC - sounded better after being powered on for about 3-4 days. After being turned off for a day or more, they've always sounded thin and have rolled off highs and lows. At least to my ears anyway. From my experience, its more obvious and takes a little longer in digital gear than amps/pre-amps.
I don't own a BDA-1 or a BCD-1, so take this as you will. I wish more of these things had stand-by switches on them to save a bit on energy, yet keep 'em warm. Amps especially. If my NAD gear had a standby mode, why can't my current gear? No offense to the Bryston engineers.