Long---
I just read this thread, and it's kind of old, but here's my 2 cents worth!
Shooting from a bench, most of the top benchrest competitors shoot the "free recoil" described above. If you can't get used to that technique, then you need to determine where the pulse beat is coming from.
Stimulants, such as caffeine and nicotine, can really give me a ferocious pulse at times, as can really hot weather. Sometimes, putting my sling on slightly wrong, (I'm an NRA HighPower shooter), can contribute to a pulse beat from the brachial artery in my arms. When you analyze the pulse beat, it's usually because a major artery is somehow constrained. For instance, when you are sitting at the bench, maybe changing the position of your rear end and legs could help. Your femoral artery runs down the inside of your legs, and I have personally found that it can give a pretty bad pulse bounce if my legs are positioned wrong. Maybe trying to sit differently on the bench would relieve some of this. Likewise, when I shoot sitting, I unbutton the top button of my pants. This helps quite a bit in reducing the pulse beat. If your neck is bent as you lean over the stock on the bench, you might be "kinking" the carotid artery in your neck. If your arms are really bent, you might be "kinking" the brachial artery.
Try different positions at the bench, with the emphasis being on not bending the major joints of the arms and legs so that your blood flow is not constricted.
BTW, I have heard that Mountain Dew has twice the caffeine of strong coffee!