Use wire wool and light oil to rub off the rust. A lot of people on here will tell you to use fine wire wool but I have used medium and coarse wool for 40 years with no problems of the blueing being removed. The barrel bores do not usually rust due to the lead running through them and slight vaporised oil from the compression chamber being deposited. You can run a phosphor bronze brush through followed by thin cloth on a jag and see if there is any brown rust on it. Always apply a thin film of lube on your rifle after drying it. In the Marines I used to wash my SLR in the shower after exercises in the mud and it was never rusty.
Baz
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BE AN INDEPENDENT THINKER, DON'T FOLLOW THE CROWD