The resort shuttle runs from 10:00am until 5:00pm. From late April thru September there is also a free "Dunes Buggy" shuttle that serves the Palmetto Dunes area (where the Disney resort is located). It runs from 8:00am - 9:00pm.
It's just over a mile to the beach and is an easy drive (parking is available at the beach house), but is also very doable by bike and even on foot.
The resort has a wonderful recreation department with activities for all ages - including adults. There are a variety of nature programs offered by the resort naturalist, crafts, Kids Night Out, Teens Night Out, campfires, storytelling, magic shows as well as many water related activities from the resort. This summer they even offered cooking classes with Robert Irvine - host of the Food Network show "Dinner: Impossible" and who owns a restaurant near the resort -
"EAT!" .
Enjoy!