I will be flying into Kunming and I want to take the bus to Dali Old Town, where do I get the bus?

The West Bus Station have frequent buses for DL.

I apologize for not being clear. How do I get from the airport in Kunming to the West Bus Station?

From the airport, you can take the shuttle bus line 1 to the terminal at West Inn. Then you can walk to the Xiaoximen Bus Stop on West Renmin Road to take the bus line 18 to Yining Road Station. Get off the bus, you can see the west bus station.
Or upon reaching the West Inn, you can take a taxi to the west bus station directly. From the West Inn to the bus station, there is about 7.5km.