I'm lefty. I mount from the left. I hold the left bike handle with the left hand and the saddle seat with the right. I pick up my right leg and swing it over the top bar. I put my right hand on the right bar. I proceed to bike. Should be even easier if you have a woman's bike. Probably the young'uns have a sportier way of mounting than that. In any event, it doesn't seem to require the fine motor skills that left/right handedness tasks like writing would.

Then again, I'm nearly ambidextrous, so maybe there's something I'm missing.

According to Sheldon Brown's logic, lefties should have an an advantage since bikes are wired with the strongest brake on the left side. But I signal with either hand, figuring that motorists won't have a clue what an upraised arm means.