Trent Barton run the Transpeak Service which runs from Manchester to Nottingham and vice-versa. It operates every two hours, is approx. 70 miles long and takes about 3 hrs 50 minutes.
The journey, although long, takes in amongst other places, Doveholes, Buxton, Ashford in the Vale, Bakewell, Matlock, Belper, Derby and Nottingham.
More details of timetable can be found at http://www.transpeak.co.uk/timetable.html
One reviewer wrote..
Trent Barton 'Transpeak' (no number) Manchester to Nottingham via Stockport, Buxton, Bakewell, Matlock and Derby. Only 4-6 trips end to end, but others do shorter journeys. About 3 hours 45 mins. Another one where it might be possible to run out of superlatives - right across the heart of the Peak District - brilliant.
Another reviewer wrote
Please note that the Transpeak service is very popular with bus pass users and on busy days the coaches cannot always cope with the number of people wishing to use it. If possible please try to travel mid-week and avoid weekends and Mondays (unless visiting Bakewell Market).