There are many chain hotels very close to MCO (including the Hyatt, which is right in the airport) that offer free shuttle service. Once you move away from the MCO area, I don't think you will find a hotel offering free shuttle. None of the downtown Disney hotels offer free shuttle and neither do the hotels in the Marriott Village complex which is right past downtown Disney off of SR 535.
For free (or rather inclusive) airport to hotel transfers, you might find a package deal on Travelocity or Expedia. Although, I think most packages require more than 1 nights accomodation.
If you don't want to rent a car, you might want to consider staying onsite in a Disney hotel or motel. By doing so, you could use the Magical Express service, which is a free transfer from the airport to your specific Disney property and from Disney back to the airport. You should be able to find a lot of information about Magical Express on the Transportation Board.