Weren’t Federal Senators chosen by state legislatures prior to Amendment 17? I don’t remember quite that far back. But even if they are appointed, that’s where some money can change hands.
There are oversight committees, auditors, inspectors general, state attorneys general, partisan newspapers, etc. Give me a scenario where a federal Congressional Senator (or majority/minority leader) would engage in a quid pro quo illegal cash transfer to influence an entire legislature to vote for the Washington DC party's favorite over a local favorite.
-PJ