It is possible to get to Anuradhapura on the A9 highway from Kandy. The drive from Colombo is approximately five hours by bus; or 4 hours by private vehicle. Buses travel along this highway, as well, and there is a bus station in the Anuradhapura New Town. Train service also runs to Anuradhapura from the south, with two stations being in and near Anuradhapura.
The A9 road will lead you out of the city, and you can find buses to Kandy, Colombo, and other destinations from the bus station in the Anuradhapura New Town. There are also two train stations in and around Anuradhapura, which can take you to Colombo.