It's about a 5-10 minute drive from BLT to EPCOT. But keep in mind that driving to EPCOT means possibly needing to take a tram to the gate, depending on how crowded the lot is before you get there. If you can take the monorail (or bus if it is offered in place of the monorail during monorail down hours), you get dropped off in front of the gate. The only con about the monorail, if it is open, is the need to transfer from the resort monorail to the EPCOT monorail.