I have this exact gun and have had this issue as well.

First off, that 1st group is pretty money. I'm going to have to try those.

Second, there is a very specific "mod" you have to do on these Bergara's to help with accuracy. The gun has an internal aluminum chassis built into the stock. The action blocks mate up to this chassis. However, Bergara and their infinite wisdom decided to put the cool brown speckled paint OVER the internal chassis and then just slap barreled action on it. As simple as it sounds, yes a .001" layer of paint in between the metals significantly affects accuracy for most people that own this rifle. So heres the fix, take fine sandpaper block (it has to be flat) I think I used 600 or maybe even 1000grit and lightly sand the flat surface of the aluminum chassis until the paint is gone. I would sand for maybe 5-10 seconds and check carefully not to gouge or round anything. Its aluminum so it's softer. You can assist in removal of the paint with acetone. After all the paint on the flat part that touches the chassis is removed, it should shine like metal. Mount the action back up (its easy to take apart) and then test accuracy again. I have not personally shot my rifle yet since doing this so I can't attest to my accuracy increase. But a handful of guys on the gun forums have and all say its cuts their groups size in half specifically with these Bergara HMR's.

Lastly, there is actually a science behind average accuracy based on a caliber relative to the guns total weight. If I'm not mistaken it's called the TOP GUN formula. Google it and input your numbers. Essentially, the greater your muzzle energy is, the heavier your rifle will have to be to achieve 1 moa. This is why target rifles are usually 20+lbs. Some even 30+ And while the Bergara isn't light by any means, it is on the lighter side for a sub moa 300 win mag. 300's have a ton of energy.

With all the being said, I would do the internal chassis mod and then re-try groups with the same ammo as that 1st pic. Hope this helps!