The Weardale Railway runs between Bishop Auckland West and Stanhope. There are intermediate stops at Witton-le-Wear, Wolsingham, Kingfisher Halt, Frosterly.
However, the trains only run between Bishop Auckland and Stanhope on about 20 days per year.
Otherwise, the trains run between Wolsingham and Stanhope.
The timetasble for these trains can be found on https://www.weardale-railway.org.uk/timetables

The website for the Weardale Railway provides all the information you require.