I did some checking on Google Maps.
From Carousel, the stop on the West Side of DS is a shorter walk: It's 0.8 mi. from the Carousel bus stop, so it would be a bit farther from most of the Carousel rooms. There's a trail sort of behind the Carriage House that leads down the hill to the golf course and boat dock. (It may be closed from sunset to sunrise). It connects to the golf cart bridge across the canal. After crossing the bridge, bear left towards DS and you can cross the parking lot to the bus loop.
Here's the map.
The walk to the stop near the Hilton is 1.0 mi. As an alternative, you could take a Disney bus from Carousel to Congress Park, which is closest to the bridge to the DS Marketplace and the bus stop near the Hilton. The walk from Congress Park bus stop to the Lynx bus stop is 0.5 mi.
Here's the map.
Here's the full map including the walk and bus trip from Carousel bus stop to SeaWorld, with departure and arrival times. If you open it on a laptop, you can scroll down the left panel and open "Schedule Explorer" to see scheduled runs. On a phone, I don't think you can view the full schedule within Maps, but you can change the targeted departure or arrival time. However, you can view the full schedule on the
Lynx web site. Click on the "Schedule" tab. DISNEY SPRINGS TRANSFER CTR is the West Side stop; the stop near Marketplace will be a few minutes later. 6800 SEA HARBOR DR AND ACADEMIC is SeaWorld.