It depends on YOUR style....
I just returned from a 7 day trip with friends...
Day 1 ride up to Lyndhurst VA (got caught in a storm)
Day 2 Skyline drive, and Luray Caverns (wife wanted to, so we went)
Day 3 From MP 0 to Marby Mill (caught in storm the last 10 miles)
Day 4 Marby to Spruce Pine
Day 5 Spruce Pine to Cherokee (Bryson City, actually) (caught in storm, the last 50 miles)
Day 6 Retraced the final 50 miles, took more photos etc, went to Cherokee, and the museum. (we've done the dragon, nantahala, cherahola,foothills to death.... )
Day 7 returned to Raleigh.
Could we have done more riding each day? sure.... but we could have stopped more, as well....
Our "goal" was to have fun, on vacation. 5 riders, we took turns leading for one hour, we stopped where and when the leader stopped... I took over 400 photos, as did two others.... but that was OUR trip...
You could possibly do the entire BRP in one day..... but that's sun up to sundown and stopping only for gas.... assumming you catch all the repair crews at the right time...
Two days is pretty easy too..... but again long days, and few stops...
Three days? we started around 9 AM, and were parked for the night by 6 PM, with meals, and stops....I think the next time it'll be south to north.... and four days