You may get reasonable quality if you were to turn them in a Swiss Lathe, but exceeding carbide die quality custom bullets, is going to be a stretch. There are plenty of people trying to make a buck by turning bullets already. I don't think some small chicom cnc will get the job done. If your really serious in making better bullets, you'll need a REALLY large wallet.
Grinding them and lapping is an option, but, whats in your wallet?
Any CNC that is using ball screws, driven by electric motors, will have some error. Although very minor, it will still be there. It's noticeable when cutting threads and especially when cutting a taper or a radius. Even though they will look pretty to the naked eye there will be errors in one to the next. In the real world it usually is acceptable, but when your talking 250,000 rpm and .2 moa it will matter.
I don't think anyone would consider a lathe an acceptable means for achieving such tight tolerances.