Duitama is about 200 km northeast of Bogotá, roughly three hours by bus via the Autopista Boyacá. Buses from Bogotá's Terminal de Transporte del Norte run frequently to Duitama directly, or you can change at Tunja (50 km southwest), which has more frequent onward connections.
From Tunja, shared taxis (colectivos) and buses run to Duitama throughout the day and take about 45 minutes. The ride along the Altiplano Cundiboyacense, with green hills on both sides and the occasional colonial town flashing past, is pleasant.
There is no airport at Duitama; the nearest is El Dorado in Bogotá.