Depends how "cost effective" you want to be ...
You could walk from SSR to DTD West Side (there's a walkway behind the Carriage House, near the boat dock.) From there, you can get a public bus (Lynx) to Sea World for $2 a person, each way. It's a 20 minute ride. The depot is next to Cirque du Soleil, on the right as you face it from inside DTD.
You'd want to walk, because the Disney buses from SSR to DTD probably don't run early enough to get you to Sea World as early as you might like. If you decide to wait for the Disney buses, there's another Lynx stop on the street in front of the toy store.
The bus you want is
Link 50. You can buy tickets in advance on their website, but it doesn't save you anything if you're only making the 1 round trip. Just make sure you have exact cash for the fare box, and ask the driver to let you know where to get off for Sea World.