There are no direct buses from WDW resort hotels to the Transportation & Ticket Center (TTC), where you catch the Lynx bus to Sea World or other destinations. To get to the TTC, take the MK bus from your resort. Once at the MK, take the monorail or ferryboat to the TTC, and walk around the left corner to bus parking where you will find the marked Lynx bus stop. You should have change (coins, not a ticket) for the bus fare for each person.
There are two Lynx routes which stop here; You want the #50 bus (the other route heads east on Hwy 192 toward Kissimmee), which heads pretty much directly to Sea World (be sure not to miss the stop, but it is fairly obvious). You will not need the I-trolley (which isn't really a trolley car, of course) to get to Sea World. It could be used to reach International Drive destinations, but that involves about 6 (yes, six) transfers round-trip from your WDW resort to I-Drive destination.
You can also take the #50 bus all the way to downtown Orlando, where you can change buses to reach anywhere Lynx goes. That includes Universal, though since it isn't a direct route (or as convenient), you have to make so many transfers, and so on, far fewer people here really recommend it. But yes, it can be done.