We are arriving at Hongqiao Airport and would like to take the high speed train to Suzhou.

Well, actually, you don't need to take the bullet train. Upon landing, there are several direct long-distance buses that can take you to the destination. They depart from 09:30 to 21:00. It takes around 3 hours. And the ticket fare is CNY 84 per person. You don't need to purchase the tickets in advance. Just buy them when you arriving at the airport.