There are Upper Egypt Bus Co buses from Farafra to Cairo (LE105, eight to 10 hours) via Bahariya (LE30, three hours) at 10am and 10pm. Buses from Farafra to Dakhla (LE30, four hours) originate in Cairo and leave around 2pm or 3pm and around 2am. Tickets are bought from the conductor.
Foreigners are not allowed to travel between oases on microbuses. You must take a bus or taxi.