The Conservative MP said it was his birthday and asked the PM if she would reopen a prison in his constituency - or "just sing happy birthday?"
Mrs May replied: "I'm very happy to wish him a very happy birthday... I hope that Mrs Bone is going to treat the occasion in an appropriate manner."
The laughter forced Mrs May to pause.
After MPs from across the chamber joined in the laughter Commons Speaker John Bercow intervened, joked: "Order! I want to hear what's coming next."
Mrs May replied, borrowing one of Mr Bercow's own phrases: "Calm down, Mr Speaker."
Mr Bone made a habit of referring to his wife - Mrs Bone - in questions to David Cameron when he was prime minister:
The Speaker was forced to step in to stop MPs' laughter at the innuendo in Theresa May's response to Peter Bone at Prime Minister's Questions.