I would take a bus to either Pop or AoA, whichever comes first, and transfer there to the DTD bus.
Travel time could be up to 1 hour, including wait time for the 2 buses. Adding in walk time to Raglan Road and a 15-minute cushion, you should be at the DHS bus stop 90 minutes ahead.
Although Raglan Road is closer to PI, the 2nd stop at DTD, I suggest getting off at Marketplace and walking. The bus' travel time from MP to PI, especially in Saturday evening traffic, is likely to eat up the time saved by the shorter walk. Plus, if you're early, you can spend time browsing at the MP on the walk.
Walking to the BW, you run the risk of the bus filling up before it gets to you. You could walk to the Swan, which is the first stop on the Epcot resorts loop, but that adds about 15 minutes to the bus ride, which erases the time advantage over Pop or AoA.