For your delectation, here's an interesting depiction of the dragon, though not drawn by Tolkien, I hasten to say.
Whether or not the wings shown here are practical for landing on bridges is open to debate.
__________________
'Mercy!' cried Gandalf. 'If the giving of information is to be the cure of your inquisitiveness, I shall spend all the rest of my days in answering you. What more do you want to know?' 'The whole history of Middle-earth..
.'