Hello, Mary,
How exciting to have a Walt Disney World trip planned in 2016. Disney's Contemporary Resort has such a wonderful location with its close proximity to the Magic Kingdom and the convenience of the monorail. It is hands-down my middle son's favorite Disney resort.
Because of safety reasons, I believe that riding one's own bicycle on the path from your resort to the Magic Kingdom would be discouraged. Also, there are not bike racks at the park, so there would not be a place to leave your bike. It is also Florida law that all children under the age of 16 must wear a helmet, so a helmet would then need to be either stored in a rental locker or carried with you.
Since bicycle riding is popular,
bikes are available to rent throughout many resorts at Walt Disney World. In fact, there are even 2-person, 4-person, and 6-person surrey bicycles to rent so families and groups can ride together. The resorts with bicycle rentals have designated paths for bikes, so these would be a safer alternative.
If you have any further questions about your upcoming trip, please let us know. We are happy to help!
-Kara