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.
 

Quoted: The above without taking your eyes off of your target .

I thought about including that, but erred in thinking it would be obvious.  You're quite right, of course.

Unless your bolt-action rifle does not have a last round hold-open capability.  In that case, you will often look at the mag to see if there's anything to feed.  I always retrofit a hold-open follower on any Mauser I keep, and many others come with one originally.  

Quoted: I do mine a little defferent when shooting match rifle.(rifle never comes off the shoulder nor cheek off the stock) When shot breaks index finger comes out of trigger guard and up side of stock lifting bolt and slide over the bolt, little finger hooked to catch bolt and bring to rear. Then push hand forward, heal of hand catches bolt moving it closed and locked and right back to grip. This is done with a rolling motion back and forward. It give me time to check my spoting scope for wind change while reloading from the striper clip and at the end of the string before the targets go down. In sitting elbow never leaves my anchor point of my leg , in prone it never leaves my mat all movement is with the fore arm and wrist. Shots made standing while hunting is done the same.

Your technique is very close to the one mentioned above.  The only significant changes I see are ones that allow one to take advantage of the easier-to-manipulate match bolt.

Quoted: You are, of course, 100% correct.  But like most things "gunny", most people haven't been properly trained. When using a firearm, doing what seems "natural" is often completely wrong.  That is why training is so important. Not meaning to hijack your thread, but the British trained thair soldiers to use a very simular system to operate the SMLE .303 rifle. They were taught to operate the bolt as you suggest and then use the right middle finger to pull the trigger and then quickly operate the bolt again.  The result was very rapid fire.  The Germans, when first confronted by this system, thought that the Limeys had developed an automatic rifle. But it was only the SMLEs, operated smartly. Today's history lesson, by Old_Painless.

You're citing the Wallbridge Method of unaimed, rapid area fire that the Regular Brit army used at the Battle of Mons, at the outset of WW I.  Follow-on troops were not trained nearly up to that standard, which, IIRC, was sixty shots on a man-sized target, at 100 yds, in one minute.
P.S., the M1917 Enfield (originally made in .303 for the Brits) has a dog-legged bolt that is, like the Enfield, particularly suitable for Wallbridge fire.
That said, nearly any bolt rifle can be fired in Wallbridge-style, if desired.