sheraton does have a shuttle =- it is outside shuttle so it is expensive - like $7 to $10 per person per way?
you can get a shuttle pass (this might be cheaper) (you might have too) to ride this thing.
get a rental car or drive your own - much, much cheaper and easier. besides then you can control when you go and leave the parks.
these shuttle can be slow and they are on their time schedule not yours.
if you want Disney shuttle you need to stay at Disney.
sheraton vistana is a lovely resort with lots to do here!!!