For travel between resorts, use the parks as your transportation hubs.
From the Caribbean Beach Resort (CBR) to the Grand Floridian (GF), you can take the bus to the Magic Kingdom and then the monorail or boat to the GF.
More strategies:
Bus to Hollywood Studios and transfer to a Grand Floridian bus.
Bus to Epcot, and transfer to the monorail. Take monorail to Transportation and Ticket Center (TTC) and then transfer to monorail to take you to the Grand Floridian (it'll be the second stop after you transfer).
Taxis are usually available as well. From most locations on WDW property, it costs $20 or less to travel one-way.
For car rentals, try Alamo or National at the Car Care Center or WDW Dolphin Hotel. On our last vacation, we rented from the WDW Dolphin hotel reserving a car from National. See
www.mousesavers.com for great discount tips. Renting from this location was very easy. The Car Care Center locations will also send a complimentary shuttle to your resort to take you to arrange your car rental.
If you elect to take complimentary WDW transportation, simply allow one hour travel time.