No, there are no direct buses between the parks and DTD. You will need to transfer at a resort. I would transfer at Pop. I would allow a little over an hour, although it will almost certainly take considerably less than that.
About a five - ten minute walk from the Congress Park stop at SSR to the Marketplace end (Rainforest Cafe) of DTD. Plan on twenty minutes or more from OKW to the Westside (Cirque/House of Blues/Disney Quest) end. I'd not recommend walking from OKW to DTD after dark if you're unfamiliar with the path. You can take the boat from OKW to DTD, about a fifteen minute ride.
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