I have only so far made two trips to Bettona, by taxi from Assisi.  There are apparently daily buses from Assisi, Foligno and Perugia.

Two hotels in the centre are housed in historic buildings:

1. ✴the Relais La Corte di Bettona, in the ex-hospice of Sant’ Andrea; and
   

2. ✴the Hotel Palazzo Baglioni.
   

Osterio dell’ Oca, 3 Corso Marconi is a good place to eat.  The Relais listed above also has a restaurant, but I have not tried it yet.