The bladder that Cuky spoke of keeps the oil and air separated. Sometimes the silica gel is used in addition so that only dry air meets the bladder.
One design uses another oil chamber to keep moist air away from the transformer oil. Air>oil>N2>transformer oil. DGA from this transformer shows high O2, so this method is not as effective.
We had a bladder fail at an industrial substation (no dehydrating breather). I believe the quality of the atmosphere hastened it's demise.
I like the N2 blanket with a bottle, gages, and alarms. No bladder to fail, and if a bushing gasket should leak, it will leak N2 rather than oil, and the condition is alarmed.