Shove the bench.

Imagine the bar is immoveable; so instead of pushing it away from your body, you are pushing your body away from it (and into the bench). Just like a push-up, this will track your hands from alongside your nipple line at the bottom to above your shoulders at the top.
Push yourself away from the bar
PUSH YOURSELF INTO THE BENCH
PUSH YOURSELF INTO THE BENCH
Alan Thrall
Think about trying to push your body away from the bar. This is gonna take a while for you to really get... When it does come your bench is gonna go way up... If I have my back against the wall and I want to push John away from me and I didn't put any pressure into the wall, he's only gonna go so far. Now if I put more force into the wall AND push him, he's going to go a lot further because I have the wall to be able to generate that force from.
Elite FTS
When you're doing a push up on the ground, you're not actually pushing the ground anywhere. You're pushing yourself away from the ground. So I want you to think about that while you're bench pressing.
Alan Thrall
When you bench press, you don't want to think about pushing the bar away from you. You want to think of pushing yourself into the bench.
T-Nation
I want you to think about pushing your back into the bench. Do not push the barbell away from you!
Neversate
Once I pause, I reverse the motion by thinking about pushing myself away from the bar. Pushing yourself away may sound ridiculous, but it will make sense once you are under the bar. Again, it’s about staying tight through the whole movement. I’m able to keep my upper back locked in much better this way.
Press every rep as hard as you possibly can. In one study, pressing each rep as fast as possible resulted in literally twice the bench press gains as pressing the bar intentionally slower with the exact same training program. When you press harder, force output is higher (so training conditions are more similar to conditions when attempting 1rm loads), and you recruit more motor units, amplifying the training effect.
Stronger By Science
Feel as if you're pushing yourself away from the bar and into the bench. This will dig your traps and lats into the bench even more, providing you with a solid base to push from.
Stop thinking about pressing the bar away from you. Think about pressing yourself into the bench. Imagine for a second that the barbell was stationary (it wasn't going to move), but the bench underneath you did move. You're trying to push yourself into the bench, and what that prevents is reaching. A lot of people will bench and they'll kind of lock out... where they're reaching to finish that last rep and they lose all upper back tightness. Then they're left trying to find it, digging around on the bench.
Alan Thrall
From a very basic physics standpoint, you are not pushing the force into that bar. The amount of force you push into the bench allows the bar to go up from you. So you want to drive as much force as you can into the bench to allow the weight to go up.
Barbell Shrugged
Like a push-up
BAR PATH CHART
BAR PATH CHART
Juggernaut
BAR PATH PROGRESSION
BAR PATH PROGRESSION
Think about pressing the bar up and back over your face, back to the starting position. This position is much more advantageous for the lockout.
Creating a bar path that moves the bar over the face as you press will help you shorten the moment arm between the shoulder and bar at lockout, putting you in your strongest position. How aggressive the motion of your face is when initiating the lift from the chest will be determined by your grip width and where on your chest you are touching the bar.
Make sure you're pressing the bar up and back - not just straight up. You can also try flaring the elbows out a bit more, as this is going to get your pecs more involved... Think about lifting the bar off your chest with max speed.
Jeff Nippard
The novice lifters pressed almost straight up initially, with the bar then moving up and back more toward the top half of the lift. The elite lifters followed the opposite pattern – they initially pressed the bar up and back at the start of the lift, and finished the lift by pressing the bar almost straight up toward the top half of the lift...while elite lifters whose bench numbers continued to rise pushed the bar back toward their face to start the press more and more as their lifts improved.
Stronger By Science
What we're trying to achieve is the shortest moment arm possible. If Marissa was to touch very low on her chest and push the bar straight up from there, the distance from the bar to her shoulder is much greater, but as she pushes the bar back over her face this distance between the bar and the shoulder lessens. That smaller distance is going to be a much stronger position for her to press from.
Juggernaut
Once you've touched your chest, get that barbell back over your upper back as soon as you can. Stop moving the bar up and down in a vertical line... Once you touch your chest, press the barbell back towards the rack. Rotate your elbows back under the barbell and this will put the barbell back over your shoulder joint where it wants to be.
Alan Thrall
Once you touch your chest your first couple of inches are going to be straight up, but then you need to start actively getting the bar back towards your face. This going to allow your elbows flare a little bit more.
Neversate
If we were to press straight up from the touch point on the chest without bringing it back over the shoulder, we're gonna end up out in front of the shoulder. We're gonna have significantly worse leverage down there. So what we want to do is we essentially want to bring the bar back over the shoulders as the first part of the press and then we want to press straight through lockout.
Calgary Barbell
I don't push straight up. I push back and then up. What that's doing is shortening the shoulder extensor moment arm, which is trying to pull [me] out of extension... down towards my hips. You're going to finish above your shoulders, so you have to get back there quickly.
Barbell Shrugged