Texel is a bicycle island, and Den Burg is the place to pick up a rental. Several shops on the edge of the village hire bikes by the day or the week, with cargo bikes, electric bikes, and child seats all readily available. Book ahead in July and August. The island is flat, the roads have dedicated cycle lanes, and almost any point of interest is within an hour's ride.
Buses run from Den Burg to the ferry, to De Koog, to De Cocksdorp at the northern tip, and to most villages in between, but they are infrequent (roughly hourly in summer, sparser in winter) — fine for a single trip but slower than cycling for a day's exploring. A few visitors bring cars across on the ferry; you can manage Texel by car, but you miss the point.