Made this trip by bus. Bus stop in Foggia is near the train station. Get tickets at the Kiwi Bar on the corner across. Get return tickets there else get them in Monte Sant Angelo at the bar near the bus stop. Buses are infrequent and not reliable. Check the schedule carefully as it varies by day. It is possible to get a bus all the way but more likely you transfer in Manfredonia: I advise at the central stop near the fountain. At Monte Sant Angelo it is a 3km uphill walk to the sanctuary and castle. Taxis are scant but ask at the bar to call you one. At the shrine there is also a taxi stand, but usually empty. Again, ask someone to call you one if needed. If buses run perfectly a one way trip takes about 1:45 hours.