Not meaning to confuse the situation but just throwing
in a couple options.
We have stayed at WL several times.
One as another poster suggested is to take the bus to TTC then monorail to Epcot and walk through. Allow an hour. Or in this same regard, take the boat to MK, catch the monorail from there. This seems a little faster to me but still allow an hr. BTW, you an catch the boat at International Gateway to BW. This is where you will walk through at World Showcase to get to the BW area. If the boat isnt there just keep walking, you will beat it. If you see the boat at the dock or see it coming, wait, you wont beat it to the BW, unless you run

The IG is located between France just across the bridge, and UK. Make sure to walk towards Canada as you stroll through Epcot, otherwise it turns in to quite the hike
Or you can catch bus to MGM then take boat to BW. You will make 2 stops along the way. One at Swan/Dolphin, then BC before arriving at BW. Allow 1hr 15 mins for this.
As for BW, it is a cool place to wind down the night. Several entertainers perform on the walk while there. We spend at least one night over there each trip. Be sure to check out the Bakery and the ESPN club. You can peek into the ESPN club through its arcade thats just to the right of the entrance.
Have fun!!