The most likely reason is that a lot of black voters left the ballot blank in those counties in that race because there was no Democrat (only a Reform candidate).
Just using one of your examples, Bryant only got 48 votes more than Barbour did in Bolivar County. Keep in mind that Barbour only got 35.1% of the vote in Bolivar. It's a similar story in Coahoma, where Bryant only had 41 votes more than Barbour (who had 36.5% in that county).
This isn't actually particularly unusual behavior in the Black Belt either. In 2014's Senate race in neighboring Alabama, Jeff Sessions was uncontested, resulting in him getting 90%+ of the vote in nearly the entire Black Belt. However, when you include blank ballots, you notice how most of the Black Belt simply left their ballots blank:
According to the Atlas, Bryant's opponent was a Democrat, but it does appear turnout was way down in certain counties... which leads to the question of why that was, considering Bryant wasn't running against a third party candidate.