The cheapest way is to take the city bus to SeaWorld from Walt Disney World. The bus is #50 and the fare is $1.75 each way. Be sure to ask the driver to let you off at the front gate of SeaWorld, and ask where to pick up the return bus (also #50). For schedules and further details, visit GoLynx.com.
There are two places where you can catch the city bus at Disney World:
Ticket and Transportation Center The trip from here to SeaWorld takes about 37 minutes, stopping at Downtown Disney along the way.
Downtown Disney The trip from here to SeaWorld takes about 20 minutes. The stop for the Lynx buses is in the overflow parking lot on the far west side of Downtown Disney. If you are arriving at Downtown Disney on a Disney bus, get off at the Pleasure Island stop and walk through the West Side toward Cirque du Soleil, then around the right (north) side of the Cirque building.