In reply to mason_7:
Burbage at least is easy - the 65 bus to Sheffield stops at the Fox House Inn, and it's a short walk from there to Burbage South.
http://www.travelsouthyorkshire.com/timetables/sheffield/533.htm
The same bus gets you within walking distance of lots of limestone, Baslow, Curbar and Froggatt. (For Froggatt you could get off between Calver and Grindleford and walk up through Froggatt village.)
From Fox House you could maybe change to the 272 bus which goes out from Sheffield to Hathersage, Bamford and the Hope Valley, but I imagine from Buxton it'd be less hassle to get the train to Bamford or Hathersage.