Annot is small enough to cover on foot. The walk from the train station up to the old town takes about ten minutes; from the old town to the edge of the main boulder field is another ten. There is no local bus service.
If you want to reach the higher walking terrain or connect to other villages in the valley, a car is the only practical option outside of walking. The D908 road through the Var valley connects Annot to Entrevaux and Guillaumes; the roads are narrow and winding but well-surfaced.
The Train des Pignes allows car-free movement along the valley — you can take the train one stop north or south and walk back, or walk to a station and take the train home. This is the most pleasant way to extend your range without needing a car.