I have brifters and aero bars. My map case velcros on the aero bars, and I have seen water bottles that are designed to fit within the aero bars. I don't know of any commercially available handlebar bags that attach to aerobars. It may be necessary to use a bag that is designed for a particular aerobar.
It could be a fun do-it-yourself project. My image is of a long, skinny bag that velecros around the sections of the aero bars that are closest to the stem, and hangs just below the bars.