Shuttle Bus from Xiaoshan Airport to East Railway Station

I am flying into Hangzhou next Monday and is planning to go Shanghai via bullet train from the EAST Railway Station. Please kindly confirm if there is a direct shuttle bus service from the airport to the EAST Railway Station. On all other websites I visited, the info seems there is a shuttle bus service from Airport to HZ Railway Station only (not to EAST Railway Station) and then use Metro to go to EAST Railway Station.