Improve Stabilization, Bench Better
The bottoms-up kettlebell press is an amazing drill to improve the precision of your pressing mechanics and also to train your body to stabilize the shoulder.
Years ago I found that doing overhead work prior to bench pressing led to superior bench pressing performance, likely because it better prepared the shoulder. With this drill you can get that benefit without having to use very heavy weights, thus avoiding fatigue that might decrease bench press performance.
Bottoms-Up Kettlebell Press
Note that I'm still working on shoulder mobility. When I'm pressing with my left arm (the formerly injured shoulder) I don't yet have full range of motion, the press should be in a slightly more pronounced backward arc.
Sets and Reps
Do two or three sets of 8-12 reps per arm before bench pressing, but don't go to the point of feeling a lot of muscle fatigue. You should feel a slight pump at the most.