You have a tight and poorly functioning infraspinatus on your right side. You need to get a lax ball, a tennis ball is ok, but not really hard enough for the amount of pressure you are going to need. Basically, you find the MUSCLE of the infraspinatus, which is primarily on the posterior side of the scapula, and look around for any knots, which I guarantee you will find. When you do find a knot, you will feel the muscle light up, it should be pretty sensitive. You need to spend time putting pressure on these knotted adhesive areas, slowly moving your arm in and out of internal and external rotation can help, as can slowly kneading the muscle with very small movements. Then you need to do a sleeper stretch, youtube cressey's sleeper stretch or use the search function for cressey and sleeper stretch. I had the exact same problem, but only on my left side.
I bet you not only have issues with bench press but also Dumbell flyes, Overhead presses, Pullups, pulldowns, rows, skullcrushers and CG bench presses, just to name a few. In short, this muscle effects every upper body exercise, even isolation movements. You may or may not have noticed some of the above exercises not feeling "just right" do what I said and you will notice the difference. I even noticed a huge difference in barbell curls of all things.
Basically the rotator cuff muscles control what is going on in the shoulder, and the infraspinatus seems extra prone to problems. This will be the biggest difference maker in your upper body weight training you have ever experienced.