I've known about this for about a week but picked up a leaflet coming back from the Peak District today. The service, tagged on to the 257 route, is Sundays only during the summer. The timing of the first departure from Sheffield means that I'll be able to catch it if my train arrives at Sheffield station on time.
The route goes over the Snake Pass to Glossop and then continues to Hayfield, Chapel-en-le-Frith and Castleton. Apart from using the bus to get up onto Kinder Scout and Bleaklow I can certainly also use it to walk back from Chapel-en-le-Frith to Castleton. Depending on where the intermediate stops are there might be other viable routes back to Castleton.
Unfortunately I can't include an image of the timetable because I no longer have a scanner, but here's a link to the online timetable.
https://www.derbysbus.info/times/timetables/hul25745-sheffield-bakewell.pdf