I often get a chuckle at the folks who are seldom seen on the range until just before hunting season.
I've seen some truly and awesomely bad bolt manipulation by most of these once-a-year shooters.
Fumble fingers (with gloves, no less), and removing the rifle from the shoulder altogether.
Picking up the bolt knob with thumb and forefinger as though it's a salad fork. IGNORANCE!
It's something many of us are guilty of; there not being many good bolt-shooters these days that are willing to share the knowledge.
That being the case, here's the scoop. It's simple, really. And once you train yourself properly, you won't even have to think about it, nor look at what you're doing.
For starters, let's assume a right-handed shooter, shooting standing. The other positions are similar, with but few changes.
To load a new round:
Do NOT remove rifle from shoulder, do NOT remove left hand from foregrip. DO cant head slightly to the left to clear the bolt body as it moves to the rear.
Remove finger from trigger, and rotate hand clockwise about 45 degrees, palm facing up and to the left, slightly cupped.
Pivoting the elbow, bring the cupped hand smartly to the bolt knob, pulling it up and towards the end of its travel, back. This is a natural function of using the elbow joint as a pivot point, IOW, no need to think, your body does it automatically by design.
By this time, as you are pulling the bolt back, your still-cupped hand's palm is facing you.
Once the bolt is fully rearward, turn the palm of your hand, using the wrist joint, so that it is facing away from you, towards the target.
Note: this is IMPORTANT. The palm of your hand NEVER leaves the bolt knob until the bolt is fully closed. Keep the palm in contact with the bolt knob ALWAYS. Just kind of rotate the palm, using the wrist joint, around the bolt knob. HINT: that's why most of them are spherical.
Next, push the bolt forward, and finally down with the cupped palm, while simultaneously dropping your head back onto the stock. Hand drops back to the shooting position.
Practice this evolution a few times, and I guarantee your time-back-to-target times will shrink greatly.