You can't fire cannons from a canoe and you can't bench press big weights from unstable shoulders.
The external rotators of the shoulders are important for shoulder health. But they also play a role in stabilizing the arms during bench presses and can contribute to a stronger bench.
Some guys know all this and do their best ostrich impression. They stick their head in the sand, neglect training external rotation, and play ignorant when their shoulders hurt and their bench stalls.
Other guys are more proactive. They do dedicated external rotation work and... still end up with a stalled bench press!
Why? They forget one-third of the muscles involved and use exercises which ignore how these muscles actually function during a bench press.
The rotator cuff muscles play an important role in shoulder stability. These muscles work like "active" ligaments to maintain proper alignment of the shoulder and reduce excess movement.
Two of the four muscles work to externally rotate the upper arm. These are the teres minor and infraspinatus. These both get worked with your classic external rotation, rehab-style exercises. But there's one other muscle that can contribute to externally rotating your humerus.
The Forgotten Muscle
By strengthening the posterior (rear) deltoid, you can increase your stability on pressing exercises AND build more impressive-looking shoulders.
To make your rear-delt work maximally efficient, combine it with the function of the external rotators during a bench press: isometrically contract to hold the upper arm in position. Don't go back and forth, externally rotating the shoulder as you do with the pink dumbbells in your typical rehab drills.
One Exercise to Do It All
Use the supinated-grip rear delt flye:
This exercise places you into external rotation and requires you to work to maintain this position while the shoulder moves through flexion and extension. This mimics the requirements of teres minor and infraspinatus during a bench press.
Even better, you're simultaneously training the rear delt and taking it to a fully shortened position. The arm path you take also lines up the fibers of the rear delt optimally to produce force, meaning you get a greater training effect.
Hold at the top, where the muscle is maximally shortened and the lever arm is longest. This will place high levels of tension through the muscle and develop the strength required for you to stabilize big weights when benching.
Since you're looking to develop stability to boost your bench press, using higher reps to train strength-endurance is a good choice with this lift. I suggest sets of 12-20 reps with a 2-second peak contraction on every rep.
This will develop great isometric strength in the rotator cuff and pack size onto your rear delts. The rear delts have a high proportion of slow-twitch fibers and respond really well to higher reps and long time under tension (TUT).