The bluing is a good thing. The purpose of cleaning your rifle is basically to protect the bluing, which in tern protects your rifle.
Basically, you use something like "Break Free CLP - Clean, Lubricate and Protect.", which is what I use. Its an oil. You wet a small rag with the oil and rub it on the barrel, until you are satisfied that it is clean and protected. This will leave a thin protective coat of the oil on the bluing to protect it from the air, moisture, etc. But inside the barrel, you do not leave a coat for protection. Don't make that mistake.
However if you are storing your rifle for a long period of time (months or years )and want to protect it, then there are greases that you would use for inside the barrel, which you would have to clean out before shooting.
And another thing: DON'T touch the bluing, the barrel, or any other metal parts of your rifle, with your hands/skin. Your sweat is corrosive, will leave "rust-prints". Wipe it down with an oiled rag when you are done with your rifle.
happy shooting!