I mount my bike from the left, clip in the right foot first and when I unclip it is left first.
Personally, this is a habit from having grown up riding horses.
You always handle horses from the left, mount from the left and dismount from the left. This convention arose from the days of swordsmen. I guess your average Joe Swordsman was a rightie....had his scabbard on the left leg so he could reach across with his right hand to draw his sword. It was easier to swing the unencumbered right leg across the horse to mount.
My 11 year old son is riding with me some now. I tell him to mount his bike from the left. Old habits die hard. Maybe I need to show him how to really ride and get out a couple of our pasture pets.