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No, there are no buses between DTD and any of the parks. You will need to catch a resort bus and change at the resort to a DTD bus, or take the SSR bus to the Congress Park stop in SSR and walk to DTD from there.
I'd get the first resort bus you see, as long as it's not one of the MK-area resorts. Probably best not to do the Epcot-area resorts either unless there's no other choice.
The easiest route from AK would be to hop on the AKL bus to Kidani (first drop off usually), get off and then catch the DTD bus from there. You can also get the bus a Jambo if you go there for some reason first. AKL is the closest resort to AK and the bus service is pretty good--it will take you directly to the Marketplace at DTD.
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