Winster has a pretty good bus service - about 6 trips per day each way (Monday-Saturday) but no Sunday or Bank Holiday Monday service. (Nearest Sunday buses: Darley Dale and Youlgrave).
Buses on route 172 are run by Hulleys of Baslow. You can check bus times (and the current position of each bus!) on this Timetable. Beware that Hulleys take quite a relaxed view to timekeeping: buses can leave two or three minutes before the printed times.
Hulleys' website does not show service interruptions (eg in snow), but they reckon to notify these on their Facebook page. Or you can try calling Hulleys on 01246 582246.
Note for ramblers fancying a one-way walk: some buses from Bakewell used to run via Youlgreave and Middleton-by-Youlgreave. There are no such through journeys in the current timetable.
To/from Sheffield, the fastest option is the 218 from Bakewell - taking about 45 minutes. Many services start/finish at Matlock, and can be picked up at Darley Dale - but most travel via Chatsworth, making the Bakewell-Matlock leg rather slow. From Matlock, there is little difference in journey time between the 218 via Bakewell and the x17 via Chesterfield - both take about 75 minutes.
Bakewell and Eyam Community Transport run services for “local elderly and/or disabled residents and to visitors to the area”. They operate Dial-A-Bus services from Winster to Matlock, Bakewell, Alfreton, Buxton and Chesterfield on certain dates each month, as well as a series of day trips further afield with pickups in Winster. They also hire 16-seat vehicles to community groups at reasonable prices (Secret Gardens use them for their Park & Ride service, for example).
Beware the "Derbyshire Wayfarer" day ticket - once very useful, this is no longer valid on most Transpeak Services.
There is a useful bus map available in PDF format.
The Transpeak service runs hourly for much of the day on the route Derby-Matlock-Darley Dale-Bakewell-Buxton. But be warned that punctuality can be very poor.
National Express run coaches from Chesterfield direct to London once a day and to Luton, Heathrow and Gatwick airports twice a day.