Disturbingly is the adverb: it tells you that something happens in a way that worries or upsets you, or to a degree that should worry you. “Disturbingly quiet.” “Disturbingly similar.” “The test was disturbingly easy for some and impossible for others.” Like distressingly, it is a little more at home in writing and careful speech. People often use it to flag a fact that is not just odd but wrong-feeling: too common, too easy, too close to a bad pattern. Though actually, it can also simply mean “in a disturbing manner,” about how someone smiled or how a room looked. The lighter verb sense of disturb (“please don’t disturb me”) does not really carry over here. Disturbingly is almost always the “this is worrying” meaning, not “in a bothersome way.”