I have the Demi Milan from Carry You, and I love it! I have it on my Pliko, which is also an umbrella style stroller.
http://store.carryyou.com/organizers.html
We couldn't use it at WDW because we used a backpack diaper bag and hung it on the back of the umbrella-type stroller. The backpack diaper bag was packed with snacks, diapers, wipes, hand gel, sippy cup, autograph book, extra clothes, retractable Sharpie for autographs, etc.
I carried an Overland Equipment Placer with valuables (cell phone, camera, money, tickets, lip gloss, etc.) It is a smaller bag, and I kept it on at all times (on rides, at restaurants).
To get on the bus, you have to unload your stroller and fold it, so it is easier if everything is in one place (in one bag).