Unfortunately, there are no direct buses or other transportation from DHS to DTD. That means you have to get yourself from DHS to a resort, then transfer to a bus to DTD.
Three of the better options would be to take the boat to Swan/Dolphin and catch a bus there, walk to BWI and catch a bus there, or take a bus to SSR's Congress Park stop and walk to DTD from there. For planning purposes, I would use 60 minutes of travel time as my basis.
You can do it quicker by car, if that is an option and you are so inclined.