If you are in the front of Epcot, taking the bus is going to be the fastest way. Otherwise, you have to walk through Epcot, and out the backdoor, which will take you about 20 mins, or possibly more.
If you exit Epcot, via the International Gateway, you can decide whether to take the boat, or walk, depending on the boat 'situation'. Now...if the boat is there, loading, then get onboard. It should be just about 25 mins to DHS once the boat leaves the dock. It will go to BW, then to YC/BC, then to S/D and finally to DHS.
BUT...if the boat isn't in sight, or is just leaving, it will be faster to just walk. It's usually about 20 mins between boats...so you have to add on wait time to the boat ride time...could take almost an hour from Epcot to DHS.
The walk, from the Intl Gateway, to DHS is about 20 mins. My friend and I got to the boat just as they were closing the doors. They yelled that another boat would be there in 20 mins. We yelled back that we would beat them to DHS...Highly doubtful was their response. Well, the last we saw of that boat was when we turned to cross the Village Green at BW and the boat was headed to YC/BC. The boat had beat us to BW by about 45 seconds. The next time we saw the boat was as we approached the entrance to DHS, and the boat was just coming around the bend....we beat them by about 5/6 mins...we were through bag check when the boat go to the dock.
One year, we were finishing up our day/evening at Epcot and watching IllumiNations...it was the terrific holiday ending. But, I also really wanted to get to DHS before they closed so I could see the Osborne Lights. So, we finished watching IllumiNations and then very quickly walked to DHS...more of a race walk really. But, I made it to DHS in just about 15 mins from Epcot. I was severely out of breath, but I got in.