Bus Travel in Portugal

Rome2Rio.com is a good first step toward answering this type of question. It shows the trip can be made by connecting in Leiria. If you drill down, you'll find the names of the bus companies on the routes you're interested in--at least those Rome2Rio knows about. The links sometimes take you right to the schedule, but not always.

Rome2Rio is not always complete, and I wouldn't trust the fare information, but it generally gives you a decent idea of that is available. Sometimes simply Googling "bus Fatima to Nazare" is productive because someone else will have asked the question fairly recently on a travel forum somewhere, and Google will turn up the question and answer.

In many countries (haven't been to Portugal recently) bus services drizzles to near nothing on Sundays and holidays, so day of week may be a factor. The best thing to do is to seek information at the bus station (better) or the local tourist office as soon as you get to Fatima.

Rick's Portugal guidebook indicates 3-4 buses/day on this route (1.5 hours), fewer on Saturdays and maybe none on Sundays. The closest stop to the basilica is called Cova de Iria. Confirm details at http://www.rodotejo.pt/horarios/todosresultados/0418/0405/1/0.