I will likely sound like a heretic, but 3 to 4 inch three shots groups might not actually be "horrible" - you can likely improve on that with practice or some minor "tuning" - my own experience would question the use of the bipod - I have never used them - I understand they bring their own issues and techniques. My own "sighting in" and "bench resting" - such as it is - has been with sandbags under the forearm. Some "boomers" - like my 338 Win Mag - I now have to hold that forearm with my off hand - many lighter ones - like 308 Win - I hold a rabbit ear sandbag with my off hand, under the butt stock of the rifle - squeeze that bag to get the sight picture, and fire - rifle will lift a bit, but I am apparently still strong enough to hold that with my shooting hand grip. That "one hand" technique was basically a disaster in multiple ways when I tried with the 338 Win Mag, so I don't do that any more with rifles with some "buck" to them.
My last time out to check scope settings, I took two rifles - that 338 Win Mag with 225 Accubond loads and a Leupold M8-6x scope. Other rifle was a 9.3x62 with 250 Accubond loadings and a Leupold M8-3x scope - both rifles produced multiple triangle three shot groups - about 3/4" hole-to-hole-to-hole - from sand bags. About as good as I can shoot any more, or tune them. Both ended up sighted in with the three shot groups centered about 2" high at 100 yards.
If my own wife's experience at the time - late 1970's (?) is any comfort - was many hundreds rounds fired by her from her deer rifle over the summer - she took her first deer with one off-hand shot, though, as did our son about 13 years later with the same rifle, so I am a big proponent of actual "trigger time" - hundreds of rounds is minimum - thousands of rounds likely is better - and even .22 rimfire count in that!
To put in perspective - a deer has about a 10 or 12 inch kill zone, when viewed from the side - so your results likely adequate for 300 yard deer kill. I doubt in 50 years that I have ever fired at an unwounded deer that far away - I still think 250 yards is a "long shot" to make in the field - but others may have had different experience.
I do have and use a Leupold brand RB-800 8x32 range finder (binoculars) when I am hunting, so my field yardage "guesstimates" are not likely too far off - no doubt there is more modern items that might range better - but is what I have to use.
A discovery that I made about using sand bags, if they are new to you - I likely read about this somewhere - apparently I seldom get "unique" thoughts that someone else has not already tried! Was with a Ruger No. 1 which has separate fore arm stock and butt stock - I would grasp the forearm more or less like for off-hand shooting, then rest back of that hand against the sand bag stack - to steady that hand - was deliberately NOT trying to make a "hand sandwich" - I did not want the forearm on top of my hand on top of the sand bag. It seemed to make a difference for me on targets, so how I do that now - rest the back of that off hand against the sand bag stack - the rifle fore-arm actually does not touch the bags - if I have to grab hold of that fore-arm on a bench to handle the recoil.