For much of my life I have been shooting a very nice precision rifle. It's a rifle I shoot hundreds of times at each practice session and have likely shot tens of thousands of times in my life. I attribute my marksmanship skills and my quick on target ability to this practice rifle. Many will likely be shocked hearing this from an African Professional Hunter! The rifle is a barrel cocking air gun. I have similiar or identical optics on them to my hunting rifle and practice with them all the time. The shooting is nearly silent, dirt cheap, deadly accurate, and easy to do just about anyplace.
Sure I shoot a firearm nearly every week. However the air rifle practice with a 9 pound gun shooting lead pellets nearly the same speed as a .22 rimfire using the same scope is a wonderful and very productive means of practice. High quality air rifles today weigh more then a centerfire rifle so the steady hold you get with practice makes the usually lighter centerfire rifle much easier. Being able to shoot 100's of shots with no pounding recoil, muzzle blast and low cost is going to assit you in target location time, and trigger control.
I can't even count the amount of guys I know with a huge collection of firearms they never shoot. Several have many thousands of dollars in Expensive guns and scopes but never have the chance to shoot them all. I have told many of them to buy a nice quality air rifle and shoot all you like right at your house. When they hear the rifle will cost 300-500 or more dollars without a scope they freak out exclaiming it's an expensive pellet gun! Well maybe so but what is the cost of all those unused rifles you have stocked away? What is the cost and time involved with the reloading? What is the cost and time of travel to get to the range?
The expensive air rifle will give you the time and practice needed to become an expert rifleman in a short time. Consider getting a trigger scale to make the airgun and your centerfire hunting rifle use the exact trigger pull. Then use the same scope. Once you shoot several thousand rounds of airgun pellets you will have a renewed confidence in your centerfire rifle without the punishment and expense of shooting it an equal amount.
Nothing takes the place of your actual centerfire practice but the air rifle will get you tons of cheap and easy pracitice. I know My skills as a marksman started with my Sheridan air rifle in the 60's and 70's. I doubt those millions of pumps I must have put through that old rifle were wasted time now! By comparison there are air rifles made which require one simple cock of the barrel which are going to give you more power and accuracy then the Old sheridan and Benjamin guns of our youth. They also accept scopes and custom trigger adjustments.
