If you just got it re-blued, the red color you see may be from the bluing process and not be actual rust.
Gunzilla will do a pretty fair job of removing it. I've seen a sectioned shotgun barrel with actual surface rust it had been used on, and it did remarkably well at cleaning it up. Using the Butch's Bore shine or Shooter's Choice or almost any other cleaner will also remove most of the red bluing if you use a brush. Shooter's Choice mixed with Kroil for added penetrating properties has been used by benchrest shooters for years.
Check with whoever did your bluing. They generally avoid putting rust in the bluing bath, so he may have dealt with the pitting already.
If the bore actually is pitted with real rust, you want to be sure to kill it all the way down in the pits, and not just at the surface, or it will continue to migrate through the steel until it makes a hole. I've been experimenting with a couple of new products I can recommend. These are
Rust Release and
Evapo-Rust. They are non-toxic and water-based and work by chelating the rust with organic molecules. To use them, you would plug your bores with neoprene stoppers, fill them carefully with the liquid and let them sit overnight to be sure of addressing the deep rust. A blackened surface will remain behind. CAUTION: These products will remove bluing (all rust removers will, that I am aware of) so you have to use them carefully. To fill a shotgun, a plastic watering can with a long thin spout should prevent spillage. If you get any on your new bluing, rinse it off immediately. It works slowly enough that you should have time to do that. Keep a damp rag and a little formula 409 at the ready.
The chelating rust removers are rinsed out with water. I would pour boiling distilled water down the tubes for final rinse, followed immediately by a dry patch. The heat will flash dry and leave a micro-thin blue oxide layer on exposed surfaces in its place. A water displacing oil or rust inhibiting (Birchwood Casey Sheath or LPS-1) substance afterward, followed by your regular gun oil to prevent new rust is recommended.
After you are sure the barrels are rust-free, have a gunsmith who knows shotguns take a bore scope to them to determine whether the gun is safe to shoot? Modest pitting from the middle of the tubes forward is far less significant than pits near the chamber end where pressure is much higher.
Nick