if there is a bus between Ganyu County in Lianyungang and Tai'an or Taishan.

As I know, in Ganyu South Bus Station, there are two direct buses to Taian, leaving at 07:40 and 10:10. Hope you can catch that.

The bus from Ganyu drops you outside the South End of Tai'an.
Walk down from the toll booth. Go right onto the highway and then take a taxi from there or walk further down and grab a bus to get into town.
I took a cab and it cost me 15 yuan to my hotel at the base of Taishan. It should cost 20 max to Taishan, if they measure by the meter.