The Bastei is a popular tourist destination in the Saxon Switzerland. It offers spectacular views, many hiking trails start here and you can see the remains of an old medieval stronghold.
There are public buses that take you up to the Bastei from the surrounding towns. Another possibility is the Bastei-Kraxler, an old refurbised bus that takes you up from Wehlen during the summer month (first departure at the marketplace in Wehlen at 9:30am, from then every hour). The ride takes about 20 minutes and returnes to Wehlen every full hour (from 10am to 17am).
There is a transfer service on the street of Kurort Rathen. It operates a minivan to transfer travellers between Kurort Rathen and Bastei. After getting off the train, cross the river by boat. Follow the street and then you'll find the sign. No specific schedule. It departs when you need it. 12EUR/person. Not sure if it operates during the winter.