We will also arrive at PVG Airport at 12:05am. What bus should we take to go to Putuo Shanghai?

According to your landing time, you can still take airport shuttle bus Night Line and get off at East Yan'an Road Middle Zhejiang Road first. Then take a taxi to your destination in Putuo. Or you can provide the detailed destination in Putuo. Then I can find the public transportation for you.

It’s in Modena by Fraser Putuo

Well, like Anthony said above, you can take shuttle bus Night Line to East Yan'an Road Middle Zhejiang Road, then you need to take taxi to the hotel. If you want to take taxi directly to it, it costs around CNY220-CNY250.