"...I called him the son of a black woman."
I doubt that Abu Dharr said "son of a black woman" because he himself was
black-skinned. Read this description of Abu Dharr:
It is related by Ibn Buraida that he said:
"When Abu Musa came, he saw Abu Dharr and he (Abu Musa) began to honor
Abu Dharr. Abu Musa was thin and short and Abu Dharr was black-skinned
with thick hair. Abu Dhar said to Abu Musa: 'Get away from me!' And Abu
Musa said (to Abu Dhar): 'Welcome my brother.' And Abu Dhar said to Abu Musa:
'I'm not your brother! I used to be your brother before you became a governor!"
فعن ابن بريدة قال "لما قدم أبو موسى لقي أبا ذر فجعل أبو موسى يكرمه
وكان أبو موسى قصيرا خفيف اللحم وكان أبو ذر رجال أسود كث الشعر
فيقول أبو ذر إليك عني ويقول أبو موسى مرحبا بأخي فيقول لست بأخيك
.إنما كنت أخاك قبل أن تلي
The issue at hand between Abu Dhar and Bilal was not about colour. It was
because his (Bilal’s) mother was a non-Arab speaker, an Ethiopian.
Abu Dhar said:
"There were heated words between me and a companion of mine (meaning Bilal)
and his mother was a non-Arab speaker and I insulted her. The Prophet (SAWS)
then said to me: 'Did you insult so-and-so?' I said: Yes. He (the Prophet) then
said: 'Did you mention his mother?' I said: He who insults people mentions their
father and mother. The Prophet then said: 'You are a person with ignorance in
him.'"
This is found in Siyar A'lam Al-Nubala by Al-Imam Al-Hafidh Al-Dhahabi.