You can catch the 8 bus anywhere on I-Drive and run down to Sea World. From there, catch the 50 bus to DTD. Ask for a transfer when you get on then you only have to pay once - $2. Buses run about every 20 minutes.
The 111 also runs from Sea World to Downtown Disney. (And a 42 will take you from the other side of the Hilton Garden Inn at Sea World to I Drive, but therefor involves a 3 min walk to change stops).
The 111 is faster than the 50 from I-Drive but you can pick it up at any point from just after the convention center (near the new Hilton hotel) to the seaworld turnoff. It then uses the same stops as the 42 on the way there and if you change at the same stop on the way back it is about a 30 yard walk to the stop.