Hi, is there a bus I can take from Suzhou directly to Shanghai Hongqiao Airport?

Yes, there are direct long-distance buses. You can take it from the North Square Bus Station. The schedules are from 6:00 to 17:30 at intervals of around half an hour. It costs CNY 53 per person.
The trip takes around 1.5 hours.
As I know, there is no limit about the luggage size. In general, there will have enough space to put your luggage on the bus luggage carrier. Don't worry.