The buses do stop at YC first. When I was at the BC over Labor Day weekend, the waits for transportation at the BC were terribly long...especially for MK. There was a late afternoon when there were probably 40+people waiting for about 45 minutes. When a MK bus finally approached, there was only standing room available, and only about five people could board that bus.
When I was recently at the YC, our empty bus pulled up for one of the parks and quickly filled up...so much, so, that we ended up having an "express" bus to the park, as there was no room for anyone else. Part of the demand depends on how busy the resorts are. If it seems really busy at the parks and resorts, it may be worth the walk over to the YC to catch a bus.
I believe that the YC bus stop is still at the Convention Center, due to construction in front of the YC; maybe someone can confirm current bus location for YC.