Mine are side-specific, but if using only one it goes on the left side.

I'm right handed, always mount from the left, typically bail to the right (away from traffic), and have a rear mounted kickstand on the left.

I like being able to get off the bike, drop the kick stand, and have the bag there to conveniently dig through. Then again, I never reach in to my bag while stopped at a red light or anything; they are for transporting purposes only. If I need quick access to anything, I'll hook up the handlebar bag quick before I go.