Local Monsanto – Idanha – CB
Public bus transport in this part of the country is run by Transdev.
Itineraries and schedule on their website
https://www.transdev.pt/horarios/beira-baixa
Note that some connections only run during school term, so best to enter date to avoid disappointment.
Train
Nearest station is Castelo Branco. Consult schedule and book tickets on https://www.cp.pt/passageiros/en
(It used to be only journeys that included at least a part on Intercity were bookable online, but not those completely on Regional trains, but this may have changed lately.)
Booking several days in advance typically yields a significant discount.
If you’re booking a train to get to Lisbon airport, get off at Lisboa Oriente and take the Metro (Linha Vermelha), it’s 3 stops to the airport.
Long distance coach
https://www.rede-expressos.pt/en
For travel to Lisbon or Porto airports, note that buses either end in Campanha or Aeroporto (for Porto) respectively in Oriente or Sete Rios (for Lisbon), so you want to allow time to get to the airport.
Rome2Rio is usually a good, up to date, source of info on further travel options: