The Steel bridges that are intended to rust over lightly and then stop rusting have to exist in a fairly dry area where they can actually recover from a moisture cycle too. The grade of steel is A588, also known as weathering steel and "Corten" is the common brand name, similar to how Band-aid or Coke can be universally applied with lots of actual other manufacturers. I personally inspected and was involved in the closure of several A588 trusses in Cuyahoga Valley National Park along the old Carriage Trails. The park service placed these in areas that are under either tree cover or snow cover with minimal sunlight and not a lot of air flow. They also failed to remove the debris (leaves, sticks and dirt) that accumulated in the lower chord members and panel points so the steel never dried out. The corrosion then continued and section loss occurred so after a series of routine inspections they were identified as having a loss of capacity so we had them closed.
There is currently an AASHTO and FHWA led investigation on A588 constructed bridges across the country because it has been identified that there needs to be a minimum air gap / clearance from the ground and traffic. Another issue identified with them was lower clearance structures over roadways that constantly received overspray from vehicles passing below, and even worse in areas with heavy salt / brine use. These structures were showing continual corrosion similar to the issues with debris or low ground / moist area clearances.
Overall, weathering steel is intended to work by having an initial "patina" corrosion phase that is tight on the surface and prevents additional moisture and oxygen (because oxygen is required for converting to Iron-Oxide) and the corrosion phase should stop. This is functional if the components are exposed to moisture occasionally and dries quickly. Some other issues with weathering steel is when the rolling mill scale remains in place, it allows moisture to be trapped behind it causing pitting and localized section loss as well as weathering steel usually requiring the ends of the beams to be painted below bridge deck expansion joints due to the joint seals leaking and not often being resealed or replaced in a timely manner, often due to the required lane closures and abatement processes.
When used in the correct application, the intent and function is absolutely wonderful. I know of a bridge that is mostly highly elevated deep girder spans over traffic, a brackish inlet waterway, and even the cross girder piers are made of it. However, where the structure declines in elevation and is closer (sub 25 feet) from the ground and marsh, there is already corrosion and repairs planned just because the air doesn't flow and the constant evaporative effect and occasional wind blown salt mist just don't mix with raw steel.
I have seen 1 fully built stainless steel bridge. It was expensive and its awesome. The hardware as 400 series though so it looks terrible with its patina rust.
I also inspected two Aluminum beam bridges outside of Phantom Ranch in the Grand Canyon... they have "Reynolds Aluminum" stamped in them which made me laugh to think of it being made of "tin-foil" and thats how they had to get them down there. I actually don't recall how they transported those into the Canyon, but I do know that the Black Trail Bridge cables were carried at night on the shoulders of men as they walked the South Kaibab trail. That was a fun bridge to inspect too.