bounce has 14 distinct synonyms spread across 5 of its 10 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its one recorded opposite is clear.
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.
hit something so that it bounces
“bounce a ball”
refuse to accept and send back
“bounce a check”
eject from the premises
“The ex-boxer's job is to bounce people who want to enter this private club”
Synonyms, antonyms and the broader and narrower relations for bounce come from Princeton University’s WordNet. Full sources and licences.