Wyndham Bonnet Creek has regularly schedule transportation to the parks and Downtown Disney but not to the airport. If you'll have someone in your party over age 25, and there's more than two of you, it's probably cheapest to look for a deal on a car rental.
If you'd have the higher priced, younger driver rates and especially if there's only one or two people traveling, it may be cheaper to use a service or just rent the car for a day or two on either end of your trip. Some of the Downtown Disney area hotels are car pickup/dropoff locations and Bonnet Creek has free shuttles to Downtown Disney. This could be a bit time-consuming but may be worthwhile if you'll have a longer stay during a higher priced time of year, allowing you to do a little grocery shopping at the beginning and souvenir shopping at the end of your trip.