WordNet records no synonym and no antonym for bate. It is the only member of each of its synsets, 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.
moderate or restrain; lessen the force of
“He bated his breath when talking about this affair”
flap the wings wildly or frantically; used of falcons
soak in a special solution to soften and remove chemicals used in previous treatments
“bate hides and skins”
Synonyms, antonyms and the broader and narrower relations for bate come from Princeton University’s WordNet. Full sources and licences.