I think I may have a few ideas of things to try. These are some of the range habits I have formed and help me get calm.
After I set up targets and walk back to the bench, I unload my gear. I get really excited at this point and know I am in no condition to shoot. The first thing I do is approach my rifle straight from behind. Make sure its unloaded. I take my position on the bench and establish my shooting position. I focus on setting my positions and getting comfortable with my rifle in the ready.
I run first focal plane so my next step is making sure my diopter is correct and I'm not seeing any reticle shift. I move my head side to side and adjust my range dial until i do not see my reticle shifting at all when I have it on the center of the target. I close my eyes for a few seconds and take a few deep breaths. I open my eyes and make sure I am still on target and my scope is all in focus and I have a full sight picture. I hold that for about 20 or 30 seconds taking long deep breaths. Once my heart rate is down I close the bolt and center everything. I do dry fires for probably 2 or 3 minutes making sure everything feels good. I make sure I see no poa shifts on my trigger pull. Usually if I see a slight shift it's because of poor trigger follow through. When I know I've got that all where I like it, only then do I chamber.
My next step is making sure I pull the rifle back into my shoulder pocket. I nose the barrel slightly down as I press into the bipod to load it up. I hold that pressure and chamber a round. I close my eyes from a moment and take more deep breaths. I open both eyes, ensure everything is still on zero and pressure the trigger. I hold that pressure until I fire. I make sure I follow through on my trigger for a second or so and let off.
You may try that whole series of steps and then get up, walk behind the rifle and take some breaths. Once you feel comfortable, repeat everything above. Give yourself 2 or 3 minutes between shots. Don't worry so much on results on paper, but focus on good habits.