I have never had shoulder pain from bench press or shoulder press with BB. But last year I hurt my shoulder on an incline bench machine press and was in pain for nearly two months, barely able to bench press an empty bar for a month. In contrast, I could lift some weight with the KB, barbell shoulder press, and incline bench press. Which led me to the conclusion that in this inflamed state, the body best indicates which exercise places the greatest and most unfavorable burden on the shoulders and potential for injury. Although some people think the incline bench press is safer, it actually has a lot more rotation in the shoulder joint compared to the normal horizontal bench press.
I like bench press and incline bench with dumbbells /with a weight like 8-10 reps or less/, but I find the preparation for the exercise very awkward when I have to pick them up and lift and adjust to the starting position. And after finishing the exercise. I'm uncomfortable asking other members of the gym for help. For now I have no problems with the shoulders from the bench press and the incline bench press with BB and I perform them.