For Summer 2019 there is now a new bus service that serves Edale and other popular destinations in the Hope Valley including Castleton caverns and the Ladybower and Derwent reservoirs. Ticket prices start at £4 for a single journey with a family (2 adults and 2 children) day pass costing only £12. See here for the timetable. Further information is available on the Peak District National Park website.