Is there any shuttle bus from Hongqiao airport to Grand Hyatt Pudong? Or subway? What's the cost?

There is no shuttle bus available, so take the subway.
Take the subway line 10 from the airport to East Nanjing Road, and then transfer to line 2 to Lujiazui Station. Take the Exit 6 and walk about 780 yards, you will reach the hotel.
The travel time is about 40 mins, and the fare is CNY5.