When you say SS he uses it "left handed", do you mean he uses it like a left handed person (and thus in his right)?
In SS, he uses it in his right hand fro the same reason his sword is in his right hand - for the motion controls. Yes I'm aware, typically right-handed peoplewould use a bow in their left hadn, but in the game, the wii remote was used for the sword AND the bow.
When aiming the bow, you could hold it up vertically like a bow to aim, and pull back on the nun-chuk while holding C to quick charge, and release C to fire.
Thus, to simulate that in game and match your motino input, bow was in the right hand.