From Brescia, there's regular direct train service to Capo di Ponte (€7.30, 1½ hours). From Bergamo, the trajectory is more complicated. Take bus line C to Boario Terme station north of Lovere and transfer there to the F27 bus (or a train) to Capo di Ponte (€7.55, 2½ hours).
By car, it's a fairly direct path up the SS42 from Bergamo to the Valle Calmonica. The 80km drive to Capo di Ponte takes about 90 minutes.