BWV is my home away from home, so this is something very familier to me.
You have two choices as has already been stated. You can exit Epcot at the International Gateway. This is between GB and the bridge over to France. If you see a boat there, and it is boarding, then hop on. It will take about 25 mins for it to make the run from Epcot to MGM...stopping at BW, YC/BC then the S/D, before heading to MGM. If there is no boat in sight, it could add another 20 mins to your total time.
I usually just walk. So, as you leave Epcot, go straight. When you get to the bridge, on your left, go left. This will take you past BW, on the left, with the lake on your right. When you get to the Village Green area, go to the left, going through the 'tunne' that runs between the health club Muscles and Bustles, and Wyland Galleries. This takes you to the pool area....cross through there, to behind the pool. You will see a walkway, go left. The S/D will be across the canal from you. You are on the walkway to MGM at this point. Just keep following it, you will go under a bridge, and then you will come up to the parking lot for MGM. Keep on going, you will see the boat dock to your right, with the buses to your left. AT this point you are at the entrance gates to MGM.
It should take you about 20 mins. to make the walk. ...25 if you amble along.