Well, unfortunetly, there is no bus to Fantasia Gardens.
Best way to get from Resort to Resort is to go to the closest available Hub, and transfer. A hub is a theme park, or Downtown Disney. One thing to keep in mind... Don't use Epcot as a transfer point for the Epcot Resorts, because you'd have to walk all the way to the back of the park.
Getting from WL to BW via Disney Transport won't exactly be lickety split... Using either MK or Studios as a transfer point will require a boat ride on one end... and that can slow things down a bit. However, both the MK and the Studios boats are nice rides. If you use Studios, my advice is to get off at the Swan/Dolphin, and walk across the bridge.