I'd suggest you use 'briber' and 'bribee', although the second does sound odd. Both would be acceptable in formal writing. I can't think of any others, I'm afraid, so if you find yourself needing to use these words too often in your work, try to rearrange things to use an alternative construction. Possibilities are: the one... the other; the former...the latter; those who offer bribes...those who take bribes.
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