I let Bot draft, I get on avg 3-5 wins per arena match.
But with Hunter/Mage/Priest I have noticed the Bot drafts with Better Logic. (or Guesses? not sure what Bot Uses to draft arena cards one over another)
For these classes, giving me an avg of about 5-7 wins with Bot Drafting.
Thing to remember is its all RNG:
RNG Hero at start
RNG cards during Draft
RNG on if you get 1 or more Legendary cards during draft
RNG on who you fight against
RNG on what cards you get during Mulligan.
So I personally think the bot does Average as of right now. not too good not too bad. Sometimes you get Lucky, sometimes you get an 0/3 run.