Is there a train or bus from the Pudong Airport to the center of Shanghai?

Oh, you can take this chance to experience the Maglev Train.
Take it at the airport, get off at Longyang Road Station. Then take subway line 2 to East Nanjing Road, Exit 6. After that, walk east around 0.6 miles to arrive at the Bund.
From the Bund, just walk east along Huangpu River Sightseeing Tunnel around 0.8 miles to find the tower.
After touring around, walk to Lujiazui Station and take subway line 2 to Longyang Road Station. And then transfer to Maglev Train to the airport.