1/2 MOA complete gun package for $1K
It will likely take more than 5 single rounds with a new Savage barrel. Around 5 seem to work well with a match barrel. I determined 9 single rounds for the gun above by the amount of copper removed on the 9th round and resistance to the bore while cleaning. It's amazing how much more "smoothly" you will be able to push the rod thru from round to round. A good bore cleaner such as Butch's will show limited light blue coloring indicating there is little copper left, as with the 9th round indicated above. The first rounds showed significantly more blue and resistance was greater when pushing the rod.
If you don't have a bore guide. GET ON.
As far as cleaning your Savage rifle between shootings,I don't do it with my factory Savage rifles, no way. I have found it takes 3 shots minimum to create consistent resistance for the follow on shots to have any consistency with velocity. I also live in a fairly dry region. Those factory barrels have a ton of tool marks. It's amazing how well they shoot though. I only clean when necessary usually around 50+ rounds then shoot three fouling shoots after cleaning. The guns are only stored clean in the cabinet after hunting season.
A friend last week dropped off a Savage M14. He said he couldn't get it to shoot well. The barrel had so much copper buildup it took me close to four hours of cleaning and well over 100 patches to include polishing. Afterward I was able to shoot groups in the .6XX" range. Not quite 1/2 MOA but reasonable. The point is don't let that copper build up too much and break in your barrel removing ALL copper during this process. Otherwise you may not polish all those tool marks making copper build up quicker and losing accuracy potential.