Yes, they do exist, but it depends a lot on where you are. In many cities, public bins now come with two or three compartments: one for compostable or organic waste, one for landfill trash, and sometimes one for recyclables. You will see them in parks, transit stations, downtown streets, and outside food courts, especially in places with strong waste-diversion goals. Cities like San Francisco, Seattle, Toronto, Milan, and Seoul have become well known for organics collection, and some public bins reflect that same sorting system.
That said, dual-stream or three-stream public bins are still less common than simple trash-and-recycling pairs. Curbside compost collection is often more widespread than compost bins on every street corner. The reason is practical: public bins face heavy contamination. People toss coffee cups, wrappers, and mixed food packaging into the compost side, so cities have to rely on clear labels, color coding, regular emptying, and sometimes staffed collection points to keep the stream clean.
So if you are looking for a bin that separates compost from trash in an urban area, check for green or brown compost bins, "food scraps" or "organics" labels, and compartments with small openings or bag hooks. They are out there, but they are not yet universal. The basic idea is simple: keep food scraps and compostable paper separate from landfill waste, and when the bin is well designed and clearly signed, it can work quite well.