There is no directly train from Suhou to Jiangyin. You cna take long-distance bus from Suzhou north bus station to Jiangyin. It takes about one hour and costs about 25 yuan.

I'm at Administrator Garden, how do i get there to take the bus then proceed to Jiangyin? Do you know which website I can check for the timing?

Actually, it is within 2km between the Administrator Garden and local North Bus Station, so you can take a taxi to reach and then catch a bus to Jiangyin.

I am able to search the timing at the Official Website of SZ Transportation Company, but it only has Chinese version. Anyway, buses for the journey are scheduled from 07:05 to 19:05 every 30min every day.