The bus ticket fare is CNY 84 and the duration time is about 2 hours and 40 minutes. You can easily find the Shanghai Airport shuttle bus(https://www.travelchinaguide.com/cityguides/shanghai/transportation/airport-shuttle-bus.htm) according to the road signs.

Dear Deering,

I suggest you get the train becuase it is more confortable and faster than bus and the price is 41,00 yuan so it is means around 4 Euro and you will expend is 30 minutes to arrive in Suzhou. Once you arrive in Suzhou also you will can get the taxi that is very cheap.

Kind Regards!

Taking bus indeed is most direct CNY86 p.p. (2Hrs )
If traveling more people and luggaguage can considder minivan hire or ask travel-agency for minivan-pick-up ("CNY 300 black" to CNY 600 must be posable). Train to Suzhou needs first transfer bij taxi or MRT to trainstaition; also depending day or night arrive...(MRT stops after 8pm reaching any train-station); trains also restricted travel for night (I believe). If you want the full modern transportations thrill... and arriving day-time, suggest also to consider.
a. Take 430Km/H maglev from Pudong airport to Pudong (CNY 50)
b. buy ticket Transfer to MRT line no.2 to Hongqiao tr.station (CNY 10 approx)
c. buy ticket for new highspeed-train 320Km/H G-train to suzhou
this will take you 15 minutes Maglev plus 1 Hour MRT 30 Minutes Highspeed train plus transfertime's. Tickets you can buy at ticket-machines at maglev/mrt/trainstation... For trains is always busy... so can happen you not directly possible on next train.