Our system is as follows (we have 2 kids and a combi double):
Diaper bag that hangs on the straps; "grab-and-go" back underneath with extra clothes, diapers, or whatever else extra we think we need for the day that won't fit in the primary bag.
When we get to the bus stop (either at the resort or at the park) -- I take both kids (ages 4 and 2 now). DH unclips the diaper bag and pulls the grab and go bag out from the bottom. Folds stroller. Carries it and the bags on. I take two kids. When the kids were younger, we kept a mei tai (a fabric baby carrier) that I would put the younger kid in to keep my hands more free. It's not stressful or anything. We've never held up a bus or made a scene. The grab-and-go bag makes it much easier. Don't put lots of little junk under the stroller...you'll have to take it all out to fold up.
Good luck!!