I doubt anybody is telling Bill to shut up. Everybody knows he’s the one more people like and respect and that gives him the real power. Hillary has power by coercion only. I imagine there are a couple of things at play.
1. He knows his time is limited and has come to terms with that. He just wants to live out his life in relative peace.
2. It’s been said he tried to tell Hillary what to do to win the election but she ignored him almost wholesale. I think he has just given up trying to give her advice since she won’t follow it anyway. To a degree we have all done this with a friend or family member.
3. He’s just plain tired of Hillary and wants peace from her so he stays out of the way.
Makes sense.