The easiest way is a cab. It will probably cost you around $15.
Using Disney transportation, you will need to take a bus to DHS. From DHS you can either transfer to a boat or you can take the walking path to the Epcot area resorts along the canal.
The walk is along a nice pathway, easy to use a stroller, and will take you about 20 minutes. The boat will take you about 20 minutes, if it's waiting at the DHS dock or getting close to the DHS dock. Otherwise, it might take another 5-10 minutes. The boat will stop at the Swan/Dolphin resorts first and then to the YC dock. You would exit the YC dock and walk to the right to the BC (YC is grey, BC is blue). It's probably a 2 minute walk.
The boat dock at DHS is to the right as you walk up towards the bag check at DHS. The pathway is on the right also, on the opposite side of the canal from the boat dock.