Best way would be to use Uber, Lyft or a taxi service. That would really only take 10-15 minutes once you are in the car.
If you want to use Disney transportation, you'll need to take a bus to DHS and walk or take the boat from there to BW. (I think the boats will be running again by August but if they aren't there will be a bus from DHS to BW.) You could take a bus to DS or any park, except Epcot unless you want to walk all the way through the park to the IG, but your travel time will be longer. Unfortunately, you'd want to plan for it to take up to 90 minutes using Disney transport, although in all likelihood you will get there quicker than that.
