For an easy way, you could rent a cab to drive you to Hangzhou Airport directly. It takes about 2~3 hours and costs more money. On the other hand, you could catch an express bus from Suzhou South Bus Station to Hangzhou East Bus Station firstly. It is 70RMB/adult and takes about 2 hours. Then, you could hire a cab driving you to the airport (about 100RMB and 1 hour).

Although there are direct shuttle bus from Suzhou to Hangzhou, the last one leaves at 16:00. It is a little earlier for you to leave/ However, if possible, you could catch the bus back to Suzhou when you arrive at Hangzhou Airport~