Briberies is definitely a word - otherwise we wouldn't accept it currently as rare. However, while bribes may be common in many societies, the word briberies is not so commonly used. In fact some dictionaries label bribery as an uncountable noun - i.e. one without a plural - reflecting the infrequency of use of the plural. I suppose bribes are batches of money or other rewards, while briberies are multiple acts of bribery.
An example, from singer Southside Johnny, quoted in the NY Times in 2018: "There were briberies going on. The fire inspector would come in and we’d be way over capacity, and bills would change hands." However, such examples are few and far between, so I think the word should remain rare, unless someone can come up with an offer that might change my mind.