It's pretty unambiguous in the book that Smaug was asleep (my emphasis):
It was at this point that Bilbo stopped. ... after a short halt go on he did; and you can picture him coming to the end of the tunnel, an opening of much the same size and shape as the door above. Through it peeps the hobbit's little head. Before him lies the great bottommost cellar or dungeon-hall of the ancient dwarves right at the Mountain's root. It is almost dark so that its vastness can only be dimly guessed, but rising from the near side of the rocky floor there is a great glow. The glow of Smaug!
There he lay, a vast red-golden dragon, fast asleep; thrumming came from his jaws and nostrils, and wisps of smoke, but his fires were low in slumber. Beneath him, under all his limbs and his huge coiled tail, and about him on all sides stretching away across the unseen floors, lay countless piles of precious things, gold wrought and unwrought, gems and jewels, and silver red-stained in the ruddy light.
Smaug lay, with wings folded like an immeasurable bat, turned partly on one side, so that the hobbit could see his underparts and his long pale belly crusted with gems and fragments of gold from his long lying on his costly bed. ... Bilbo had heard tell and sing of dragon-hoards before, but the splendour, the lust, the glory of such treasure had never yet come home to him. His heart was filled and pierced with enchantment and with the desire of dwarves; and he gazed motionless, almost forgetting the frightful guardian, at the gold beyond price and count.
He gazed for what seemed an age, before drawn almost against his will, he stole from the shadow of the doorway, across the floor to the nearest edge of the mounds of treasure. Above him the sleeping dragon lay, a dire menace even in his sleep. He grasped a great two-handled cup, as heavy as he could carry, and cast one fearful eye upwards. Smaug stirred a wing, opened a claw, the rumble of his snoring changed its note.