Is there a bus from Kunming that goes direct to Dali old town - ideally, to the south gate?

I am afraid that there is no direct bus to the old town.

You may take a bus to DL from Kunming West Bus Station. The buses are available from 7:20 to 19:20. The fare is CNY 110 or 137, and the trip takes about 6 hours. The buses arrive at Express Passenger Transport Station at No. 1, South Huancheng Road, Xiaguan, new town.

Upon arrival, walk north for about 0.6 mile to Zhuhai Market Station, and take bus Three Pagodas Special Line to Yita Intersection, and you can see the south gate of the old town. The bus fare is CNY 3. If by taxi, the fare may be around CNY 50 to 60.

Thanks very much Peter, that's great information.