Having looked at Derbyshire's website, IF all the services shown as supported by the county were withdrawn the following would be the remaining commercial services to the Peak District...
Derby to Ashbourne - TB Swift
Derby, Belper, Wirksworth to Matlock (but NOT Bakewell) TB 6.1
Derby, Matlock, Bakewell to Buxton (& A few to Manchester) HP Trans Peak
Chesterfield, Baslow to Bakewell. Hullies 170
Sheffield to Bakewell. T-MOBILE Travel 218
Sheffield, Fox House, Eyam, Tideswell to Buxton. T-MOBILE Travel 65
Sheffield, Hope Valley to Castleton. Hulley/First SY
also First SY Summer services to Bakewell
The above are hourly services, except 218 Sheffield to Bakewell, which is half hourly, and 65 Sheffield to Buxton which is two hourly with pm gaps.
Add to this the hourly train services..
Derby to Matlock.. And
Sheffield, Hope Valley, New Mills to Manchester (hourly weekdays from about 2017/8 under new Northern franchise)
I haven't studied services west of Buxton.
So many rural villages and tourist destinations COULD be devoid of any buses. Some of the supported services are school services so they might remain.
Not looking good for tourism by bus in Derbyshire in the future. So get your Derbyshire Wayfarer tickets while you can and explore this great county while you can!