What is the most efficient way to get to the port from Shanghai Pudong airport and the approximate cost?

Which part of the port do you want to.
Wusong ferry terminal at Songbao Rd or International passenger Transport Center at East Daming Rd..?!

You can take Airport Line 4 to Da Bai Shu and change Bus 51 to Wusong port and it will take you 2- 2.5 hours. It will be faster to take Bus 101, 116 at Da Bai Shu.

To East Daming Rd, take Airport Line 4 to Deping Rd (one stop), walking to Deping Rd Pudong Dadao Bus Station to catch the Bus 155 to Tilanqiao (6 stops). Then walk a few minutes to the destination.

Hope it helps. Cheers

One more thing. The ticket for the airport bus is 18yuan per person for the whole trip. I do not know how many will you pay for part of the trip. Sorry. For the bus ticket, it is about 1-2yuan. It will cost 45 minutes to a hour or so to the port by taxi. It may cost about 140yuan. it is not economical for you will have two taxis.