Hilton Head's a completely different type of resort to bike at, as you can connect to the island bike paths which were set-up along its entire length. As a result, bicycling is a popular form of transportation for guests to get to activities and restaurants.
At Old Key West you can only bike around the resort itself and the path to downtown Disney, as the resort is surrounded by highways with no shoulders. (Note: I have read that some hardcore cyclists bike over to Winter Park for meet ups, but they have to have nerves of steel and very high life insurance payouts to do so.) Since there isn't a lot of mileage to explore with a bicycle, most people would just rent a bike for a day or two therefore there's no need to have infrastructure like bike racks in place.
Fort Wilderness has a bit more infrastructure since guests often use bikes and/or golf carts to get around the resort.