A bit late, but as some have said I don't see a need for the bb bench press for hypertrophy particularly as we age and increase in strength. That being said, as an old fart who competes and has hurt his shoulder nearly everytime he gets over 400 (yes, been stuck low 4's for 4 years) I would say it is a mobility issue. That means almost any pressing whether flat or overhead can jack you up.
Most of us have at least some minor scapula winging. Which means the serratus can not pull the scapula into a good position during pushing moves. There are several things to test this and I am no expert, but one easy one is to put your back against the wall. Make sure heels, butt, scaps and skull are touching. Now bring your elbows up to 90° then bend at the elbow 90° like you are signaling a turn on a bike. Now try to touch the tops of your hands to the wall without any part of your body coming off.
If you can great, you may want to check a few other posture clues. But, if not I would suggest looking into diagnosing and correcting before a more serious injury occurs.
Good luck,
Hawk