Pun on words: how to quickly and accurately understand pun in a sentence?

As suggested by StephenS I am converting my comment to an answer.

"A bum " in American informal speech is something incorrect or worthless. For example "A bum note" is a wrong note played on an instrument.

Also in American informal speech "a rap" can be a criminal charge leading to arrest. "A bum rap" therefore is a criminal charge leading to arrest which proves not to be supported by evidence.

"A person's bum" in British informal speech usually means their buttocks, their 'bottom', or that part of their body in general.

The pun is a play on the AmE and BrE meanings of "bum" related to the senator's choice of hiding place for the money.