According to Juynboll's Encyclopedia of Canonical Hadith, on the authority of al-Ma'rur b. Suwayd, the mu'ammar:
We passed by Abu Dharr in Rabadha...Abu Dharr said, "I had a quarrel with one of my brethren whose mother was of foreign descent, so I vilified him as [you son of a black mother]. He went to complain about me to the Prophet. When the Prophet met me (one day), he said, 'Abu Dharr, you are someone who still displays Jahiliyyah.'"
There is more, but nothing about asking Bilal to tread on his other cheek. In fact, Bilal is not specifically mentioned, but this Encyclopedia is mostly about the Prophet's statements, so it makes sense it would not mention Abu Dharr's act of contrition in particular. And again, Juynboll does say there are variants.
As for the source, Juynboll says the most likely common link for all the variations is al-A'mash, that is, Sulayman b. Mihran.