the cheapest or fastest way from nanjing lukou int airpot to yangzhou west long distance bus st?

The convenient way is to take the airport shuttle bus to reach Yangzijiang Middle Road in YZ first and then take a taxi to reach the long distance bus station.
The shuttle bus fare is around 65RMB and cost about two hours. From Yangzijiang Middle Road to the bus station, there is about 3.5km.

it's the same suggestion if i want to go ramada casa yangzhou hotel from nanjing airport?thanks

Yes, at the airport, you can take the direct bus to YZ first. Get off at Yangzijiang Middle Road and you can take a taxi to reach the hotel in 10min.