I think the Ring would have no problem with going to a Dragon. The real reason for this not happening in The Hobbit was because Tolkien obviously hadn't thought of that yet
As for a canonical reason, Smaug was a sedentary being and perhaps the Ring thought the mobile Bilbo a better means of getting to Sauron.
Seeing how Dragons allready were powerful, think of the damage an invisible Dragon wielding the forces of the Ring (or some of them) could do!
I'm pretty sure that if the Ring,opportunistic thing that it is, thought tempting a Dragon or Balrog or Eagle or Ent or Warg or even a ladybug the best way to go, it would try to.
This begs the question,would Smaug the Dark Dragon Lord be able to destroy Sauron and take his place??