WordNet records no synonym and no antonym for bulk mail. It is the only member of its synset, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
mail consisting of large numbers of identical items (circulars or advertisements) sent to individual addresses at less than 1st-class rates and paid for in one lot
Synonyms, antonyms and the broader and narrower relations for bulk mail come from Princeton University’s WordNet. Full sources and licences.