Nokonoshima Island transport fare

Please advise which would be the economical type of "one-day pass" to travel for this route.

Is Fukuoka Tourist City Pass ( 820 yen ) feasible?
http://yokanavi.com/access_tourist_eg

I stay nearby Hakata Station.
At Hakata Bus Terminal, board Nishitetsu Bus # 312 to Nokonoshima Tosenba ( 430 yen )

By Ferry to Nokonoshima Island ( 230 yen )

( Is this by a private operator? )

Once arrive at Nokonoshima Island, take Nishitetsu Bus to Nokonoshima Island Park ( 230 yen )

( Is this the same Nishitetsu Bus company operating in Fukuoka City? )

By Ferry back to Nokonoshima Tosenba ( 230 yen )

Take Nishitetsu Bus (or subway) to Tenjin / Canal City / Nishijin ( I am flexible with any shopping districts )


Thank you.

Contrary to what may be suggested above, the Tourist City Pass doesn't cover all bus lines in the city. On the pass you could take the subway to Meinohama, then a Showa Bus to close the ferry port; or the bus all the way as you suggested. But the ferry is not covered, nor is the Nishitetsu Bus (yes, it's the same company) on the island. You can get a good preview of the ride and the Island Park:
https://www.youtube.com/watch?v=H-RmFcmhs9c

If that is all you are doing in a day though, the pass might not pay off. You might look at a subway day pass from Hakata to Meinohama, then walk (about 20 min) or pay for the Showa Bus to the ferry area. The pass is 620 yen for a weekday (less on weekends). Depending on where you do your shopping, it might be more economical.
You can also see a lot of other good places to visit in the city at:
http://www.thejapanfaq.com/fukpic.html