What clue does Bilbo reveal to the dragon?

Smaug wants to know exactly who Bilbo is.... Bilbo gives him the following clues without revealing his name.

"I am the clue-finder, the web-cutter, the stinging fly. I as chosen for the lucky number."

"Lovely titles!" sneered the dragon. "But lucky numbers don't always come off."

"I am he that buries his friends alive and drowns them and draws them alive again from the water. I came from the end of a bag, but no bag went over me."

"These don't sound so creditable," scoffed Smaug.

"I am the friend of bears and the guest of eagles. I am Ringwinner and Luckwearer; and I am Barrel-rider," went on Bilbo beginning to be pleased with his riddling.

"That's better!" said Smaug. "But don't let your imagination run away with you!"

This of course is the way to talk to dragons, if you don't want to reveal your proper name (which is wise), and don't want to infuriate them by a flat refusal (which is also very wise). No dragon can resist the fascination of riddling talk and of wasting time trying to understand it. There was a lot here which Smaug did not understand at all (though I expect you do, since you know all about Bilbo's adventures to which he was referring), but he thought he understood enough, and he chuckled in his wicked inside.