The fastest option is probably to take a taxi directly from AK to DTD. Otherwise, you will need to go to a resort first and then transfer to a DTD bus. If you do the transfer route, allow up to 90 minutes of travel time (45 minutes per leg of the journey). Otherwise, I would consider taking the bus to SSR because you can use the walking path to get to DTD. I've used the buses to get from AK to AKL and from AKL to DTD and those were pretty good (only shared a bus with Kidani). So that's another option.
In terms of getting back to CSR, you can either take a bus from DTD to CSR or take a taxi.