If you are really keen to ride a monorail, just for the sake of riding one (they are almost an attraction for some people) then take a mid-day break and ride the resort monorail around the lagoon. It takes about 30 minutes on average.
But from BWI, take the bus to MK. The Epcot resorts get a bad rap for transportation, but I use the buses and other than DTD, I haven't had any issues. I tend to have issues with DTD buses at all resorts, not just the Epcot ones (although on my BWV trip earlier this month, I only waited 10 minutes for a bus to DTD and there was one waiting at the DTD stop when I was going back, so I felt very lucky). You don't have to change transportation at any point taking the bus, so you really save a lot of time over walking through Epcot to take the monorail.