I am arriving Hangzhou airport at 1730. Is there bus service to Suzhou after 1815?

Yes, the only schedule after 18:15 is 20:15. The destination in Suzhou is at Jinjiang Inn, No.1585, Renmin Road, Xiangcheng District. The duration is about 2.5 hours. And the ticket fare is CNY 90 per person.
But I cannot find the booking page. You can buy the tickets at the airport as early as you can. Or you can try to dial ：(+86)571-96299 or (+86)512-67299950 to consult details about booking issue.

Yes, you can still have a choice. Actually, only two direct buses are scheduled for the trip daily, leaving at 14:00 and 20:15, so you can catch the latter. No need to book in advance, and it is fine to get a ticket on the spot. It shall take around 2.5h and the fare is CNY90 per person. The drop-off site is the Jinjiang Inn, no. 1585, Renmin Road, Suzhou.