Contact the coach company: the man you lent the book to might have handed it in as lost property at the end of his journey. It's unlikely that they'll be willing to give you his details because that would be a violation of his privacy. Would they even know who he was? Do they have your details, for example? Would you have any way of telling them which of the however-many people on the bus you're trying to contact? If you can pin down a specific person, you might be able to convince the company to give him your details.
It's also possible that he handed it in as lost property either at the bus station where he got off or to the police. You could try contacting bus and police stations on the rest of your coach's route.
Does the important document that you've lost identify you? If so, it's possible that he will find the document, realise its importance and try to find you to give it back.
Otherwise, as suggested in other answers and comments, newspaper ads and social media might help.
But do bear in mind that all of these ideas are long-shots.