Their sculpted portraits tell us that, up until Hadrian’s time [117 - 138], Roman Emperors were clean-shaven. (Beards were worn until Alexander the Great made shaving fashionable, circa 300 BC.)
But Hadrian chose to wear a beard, perhaps in emulation of the Greek philosophers. His portraits evidence that he broke with clean-shaven tradition and, in so doing, he apparently established a new trend. Subsequent emperors were always portrayed sporting beards.
Thus, the presence or absence of a beard will cue you as to whether the Roman bust you are looking at is of the earlier or later Empire.