Bill is going to be a free man after Hillary’s Presidential aspirations are history. I don’t think he ever really wanted her to win. They’ve stayed together only because it served her political ambitions. Now that POTUS is out of her reach, there isn’t a reason for them to carry on the facade any longer.
Thinking on it further, it would also tie him more to DC and public appearances that he's free from under his current status. He pretty much comes and goes as he pleases now but a Hill Presidency would give him requirements and restrictions he'd rather avoid.
Except for the fact that as husband and wife they cannot be made to testify against each other.