How do you bench? Do you shrug your traps? Also, maybe your left lat is a little weak than your right? I have this issue doing OHP because of a lat imbalance.
But as far as kicking the weight up, you are just gonna have to get better at doing it with your left side. Maybe do that side first? I usually kick both of my up at the same time.
Also, try doing DB Floor Presses. I was having trouble with DB Benching and I switched to doing them on the floor and they feel AWESOME. Any of the problems I had benching did not exist while laying on the floor, so I was able to focus on doing the reps very well.