You can also take the public bus to Sea World. We did this before. To do so you go to the Ticket and Transportation Center, and go to the exit, keeping left. There is a Lynx bus stop and you wait there -- you would want bus #50. the bus then stops at DTD West Side out in the parking lot, and then a couple more stop along the way. The Sea World stop drops you off outside the parking lot so you will need to walk across it, it's not bad. For the return, you walk across the street to catch the bus back to either DTD or The Ticket and transportation Center. It was if I remember correctly less than $1.75 per adult each way -- kids are a reduced fare, I think. if you take that option, make sure to take exact change because the driver nor machine will make change for the fare.
golynx.com would have more info on the schedule and fares.
It's a public bus, not a disney bus so the drivers are not as outgoing and friendly as the Disney ones, but it's an average public bus. It was the least pricey option we found, and for us it worked out well.