Surface rust.

So I took my mossberg 500 out for a weekend in the desert for a shootout. Weekend went great and even ended with 2nd place in the shotgun comp. Ended up staying 2 more days after for a get together as one of my buddies was getting married and the group wanted to camp for a few more days. Sadly I neglected my shotgun and when I had gotten home and pulled it out of the case it had collected a few patches of surface rust along the barrels. Yes, both barrels -_-

So my question is, is there a way to permanently get rid of this surface rust, or is it going to keep coming back? I use rem oil for my cleaning with some frog lube on contact/wear points for reference.