From Naha bus terminal (across the street from Asahibashi monorail station) you can take the Expressway Route bus No. 111. The trip will take about 2 hours and will cost ¥2,040. There will be many stops along the expressway on route.
The No. 111 runs all the way from the Naha airport as well and costs ¥2,160.
It is easier and less expensive to take a tour with a private company which typically includes admission to the aquarium along with other side journeys for 5000￥ compared to 5600￥ just for transport plus 1800￥ for admission to the aquarium. The ride is also shorter as you do not have to make stops for passengers although there are of course stops for other attractions depending on your tour. The tours typically allow you 3 to 3 and a half hours at the aquarium. They begin around 8 am and finish around 6pm, depending on the tour. http://okinawa.0152.jp runs tours if you would like more information. A Japanese speaking guide is also provided. Generally no English.
Okinawa Churaumi Aquarium, 424 Ishikawa, Motobu-cho, Kunigami-gun, Okinawa Japan 905-0206, ☎ 0980-48-3748, . 8:30AM-6:30PM (last admission 5:30PM). Part of the Ocean Expo Park, the Okinawa Churaumi Aquarium hosts a large tank of 7,500 m3, where large fish including whale sharks and manta rays are kept. This site is very popular among Japanese and it pays off to visit it early in the day to avoid the crowds. The Expo Park is an hour away from Nago Bus Terminal and will cost ¥860. If you are coming from Naha, there are many package bus tours for the same price (~¥4,800) and more convenient travel.¥1,800. (26.69375,127.87761)edit