...new bore brush and Shooters choice, I got some bluish tinting on the cotton patches.... still have that rusty red color though.
You will always get some "bluish tinting" because the Shooter's Choice is eating a bit of the bore brush as you use it.
Hence the "tint" when you patch it out.
Shove a thoroughly sopping wet
patch through the bore, and drop it out the muzzle. Let things just soak
for 20 minutes
then scrub a dry patch through to see if the blue is still there.
But in the end -- if the rifle loves shooting the way it is -- well, don't fix it further. Just protect it.