Most people on the Swinging Bridge will be lined up facing the upstream view, and you can't really blame them. But the downstream views, to a lazy Merced River, are worthy, too.
All the rafts in this photo probably came from Curry Village. $26 per person gets you a raft, paddles, and a free shuttle ride back to Curry Village after you've finished your three-mile float through Yosemite Valley. Rafting season usually ends in early July due to low water levels (details).