The Hobbit: The Desolation of Smaug : How did Smaug know…

that Bilbo had the ring ?

Simple question.

What's the answer ?

Smaug certainly knew that Bilbo possessed something extraordinary. The dragon seems to have been able to sense the Ring's power whether or not he could identify it. It is possible that Smaug actually glimpsed the Ring if he saw the hobbit turn invisible.

"There are older and fouler things than Orcs in the deep places of the world." - Gandalf

Smaug, said that he smelled that Bilbo carried something made of gold but far more precious.

So, the question becomes, 'what does Smaug mean when he says "far more precious"'?
Does Smaug know about The One Ring of Power? Maybe, but I don't think he thought Bilbo was carrying it.

There were 7 Rings of Power given to the Dwarf Lords, some were "consumed by dragon's fire", so maybe Smaug had encountered carriers of Rings of Power and recognized the smell.

There's no suggestion that he knew it was a ring of power; just that he sensed something magical. And it's perfectly possible to suppose that dragons just have a sense for the presence of magic in general that people/hobbits/dwarves don't.

Smaug was very old and very powerful. Being greedy and a horder of gold and precious gems, it is entirely possible he would have heard of these extraordinary rings of power and coveted them for his own horde.