The best way to start your push-emphasis training days such as bench press day is to "prime" the stabilizers of the shoulders, rotator cuffs, and upper back. The rotator cuff stabilizes the shoulder joint as well as positions the gleno-humeral joint for maximal centration so the bigger prime movers can do their jobs more effectively.
Since many lifters are spending hours sitting with a forward and rounded posture, the anterior cuff and internal rotators of the shoulder usually aren't in need of priming. As such, we need to go to the backside of the body.
The banded pull-apart and cable face-pull work well here. The key is to train a stable shoulder blade with a dynamic gleno-humeral joint, which is usually one hell of a challenge for lifters, especially those with banged-up wings from years of pressing.
The cable face-pull trains both the static and dynamic stability of the shoulder blade, along with the gleno-humeral joint, which makes it more of a "catch all" movement. Also, it involves more moving parts, which makes it a higher-level skill acquisition movement, and that's exactly what we want when re-learning how to position and stabilize the shoulders.
Program the face-pull with higher set and rep schemes of around 10-15 reps with minimal rest periods. This will go a long way to provide the active joints with the motor oil they need to function properly while making sure the prime stabilizers are all active. Stay smooth on the execution. Work the pump and "feel" the muscles working.