The Washington State bribery statue, RCW 9A.68.010 says it is illegal if you
With the intent to secure a particular result in a particular matter
involving the exercise of the public servant's vote, opinion,
judgment, exercise of discretion, or other action in his or her
official capacity, he or she offers, confers, or agrees to confer any
pecuniary benefit upon such public servant
It would take creative but not ludicrous argumentation to make the case that paying for a resignation constitutes securing a particular result in a particular matter involving the exercise of the public servant's actions in his official capacity. If you pay for a resignation so that the official is not in the Senate when a certain tax bill comes up for a vote (the result to be secured is that the official will not vote in favor of the bill, because they are no longer a senator), that would satisfy the requirements for bribery. If you just don't like the guy and want him gone, then the payment is not about a particular matter.