Hey I had the same thing just in smaller amounts on my browning bps i got about 4ish years. It was barely noticeable but now there are tiny little flecks of bluing gone. I went to a gun shop and asked. I forgot the barrel in my excitement so I described it to him and he said not to worry about cold bluing it? What do you think?
Someone on here suggested brownells cold blu product called "oxpho-blue". I am picking some of it up soon. You should also try rubbing "kroil" on it. It helps it come off quite nice. The cold blue from them says that it helps take off minor rust and its cheap and guaranteed by brownells in case you don't like it. I am just going to get the kroil and wipe the gun down and then try that cold blue stuff. If you want to wait about 2 weeks I will let you know how mine went. But I would suggest grabbing these products and try.
Your best bet to get the rust off is to use the kroil. People on here have told me that it should take that rust right off. Then if it doesn't look up to your standards, use coldblu and rub it in well.