We did a bus from Disney to sea world a few years ago!
transport will tell you what bus number to get. depending on how many are traveling and your budget - I would advise against it as it took so long to get from your resort to transportation the wait for Sea world bus then the same coming back.
I can not remember how much it cost but recall that if three people were traveling it was cheaper in a taxi.
here is a link for quicksilver but in sure there is lots of other taxi offers.
Quicksilver Tours & Transportation : Orlando airport Disney World transportation.