is there a bus from Zhengzhou & if so which bus & from where & what is cost to Baiyunshan?

Hi, I'm afraid there is no direct bus there. But you can take a train to Luoyang first, taking 2-3 h for the whole journey. A hard seat can be ok, costing around 20RMB.
Once upon arriving at the railway station, you can easily find the nearby long-distance bus station, where you can take the direct bus to Baiyunshan. The fare is about 40-50 RMB.