Snape mentions Occlumency lessons from Aunt Bellatrix (incidentally, can you imagine someone less capable of focusing and pushing out emotions than Bellatrix?), but it would appear Draco has learned other things from her as well, most notably to distrust Snape, who he's always trusted before. I wonder what exactly Draco's motivations are - is it just the desire to prove himself, or is his father a consideration as well? Does he want to atone for his father's failure, so to speak, and maybe obtain more merciful treatment for his father that way?

Either way, between the desire to get the credit himself, for whichever reason, and Bellatrix' insinuations about Snape, he isn't very enthusiastic about Snape helping. I don't think it necessarily means he's as confident as he seems, though. Surely he has to be daunted and afraid, despite his rather clever plan.