I am shooting prone. When I preload the bipod, the stability points are 1) the bipod 2) my shoulder and 3) the rear bag. The vertical grouping is pretty good, thanks to the stability of the bipod and rear bag. The horizontal grouping is adversely affected by the instability of my shoulder. My question is this, how can I preload the bipod without my muscles and elbow support affecting my shot?

You need to build a better prone position is all. Are you preloading the bipod by using only your feet? You shouldn't be using any muscles in the prone or any other position for that matter.

I agree in theory you should not use any muscles, but in practice, how do you prop yourself up with your elbows without using muscles?

If you are going to preload the bipod, you simply position your body forward into the rifle and let the weight of your body load the bipod into your shoulder. The main thing is the bipod's feet need to be secure enough to hold the weight. You should be low enough that you can still shoot with no stress in your position. I do not load the bipod when I shoot, since there are many times you can not load it up due to the ground you are shooting on. Shooting sometimes loaded up and not loaded up will cause your POI to shift, generally up and down. And if the rifle is not bedded, or the stock has some flex to it, it will mess with your consistency.

As was said the feet have to be up against something or in the ground a bit. Once you have that, get behind the rifle good and comfortable, then scoot your torso forward with your toes another inch or two. From bottom up it should be bag, stock, cheek with the weight of your head resting on the stock, elbows on the ground pointing outward from your body. You should be relaxed enough to take a nap on the stock.

Left to right problems are often trigger control and/ or breathing. Get a sight picture, breathe normal, squeeze the trigger straight back as soon as you exhale. DO NOT LET GO OF THE TRIGGER! The number one most common problem my students have is lack of follow through. Keep holding the trigger to the rear until your reticle is back on the target after the shot is over. Doing all of these things will not only tighten up your shooting, but give you the ability to witness impact, or more importantly where your shot missed so you can make a quick correction.

Thanks for the tips, if anyone else has suggestions, fire away. I shoot okay off sandbags, but the bipod needs improvement.

is you scope mounted in a way you can puts lots of weight on your stock and see through your scope. I have great success putting as much head weight on my stock pushing into the shooting bags to keep things steady.

I already pretty well put all the weight of my head on the stock, but I'll try to pay attention to make sure I'm resting my head on the stock. Thanks for the tip, that's another thing I'll be aware of...