Mears run a shuttle bus to KSC, picking up at Disney resorts. I don't know, however, if this includes DVC resorts - where will you be staying?
I took this trip a few years ago and was collected from POR in a Mears mini-bus. Just as I was beginning to think it would be a very exclusive trip for the two of us, we pulled into the DD parking lot and joined a big coach full of other mini-bus passengers for the trip to KSC

. I assumed the mini-bus fleet goes to whichever Disney resorts have passengers for them, so I'm sure the DVC resorts would be as good as any of the others, but it would be a good idea to check first!
I don't remember the exact cost, but I think it was in the region of $20 pp (or it could have been about £20 pp - I thought it was pretty good value, anyway!).
We were picked up at around 8:30am and arrived at KSC at about 10:00am. We had to meet back on the bus by 5:00pm and got back to our resort around 7:00pm by the time we'd dropped everyone off en route.
I'd definitely consider this way again if I was car-less
