Actually, I think being "First Mate" would be exactly Bill's cup of tea. He has an unquenchable thirst for attention and approval. With his wife as president he would be in the spotlight constantly, with none of the responsibility or criticism.
Also, don't rule out the possibility that Bill will end up with Hillary's senate seat.
I can't ever see him as a Senator. Too many restrictions on his quest toward earning more $$ than he can ever spend and he'd go nuts being one of 50.
I doubt the Beast enjoys being a senator. It was her steppingstone toward her ultimate goal. I'm sure she looks down on each and every one of her colleagues.