I may be in the minority here (or maybe I am just not quite as nice as the others)
But...I would say that you missed this one. The table folded to the button and its quite obvious (after the fact) that he was trying to steal the blinds. When he raises you on the river why are you reraising him back? Obviously he has something. He is not trying to bluff you at this point (and if he is, let him) I call here rather than push. What are you beating? The ace is of no value now....
I think the word 'bad beat' is often used out of context. A bad beat IMHO is when you are large favorite when the money goes in and you end up losing. This does not qualify as a bad beat although I would classify it as bad luck ($60) combined with a bad decision ($20).
I think your best move on the river is a check/call rather than betting into him. Either you induce a bluff, split a smaller pot or do not lose nearly as much.