I grew up in that area, just above Norfork Dam. Went to Norfork High School.
I would be very, very, very, very (repeat, very) careful about riding in the area.
It is quite scenic, yes. But the roads are narrow, rough surface, there are no shoulders, lots of blind spots topping hills, lots of blind curves. The population is mostly retirees and even driving around there is a big risk. Folks are not acquainted with (road) cyclists, and they won't be watching out for you. You also run the risk of being buzzed by local rednecks.
As much a bummer as it sounds, I'd say forget it. Unless you just want to cruise the back streets around Mtn. Home itself.
But if you must, take 201 South out of town toward Norfork. Lots of climbs and nice views. There are a few county roads that cross where traffic will be lighter. Or, check out heading west (by car) over toward Buffalo River. There may be some trails and such over there that I'm not aware of.
Sorry to be such a buzzkill. I will jog in the area when I visit my mom, but I do not bother with a bike.
One more thing. Locals tend to stay out of the woods in summer and it's a good idea. Ticks, chiggers, and snakes galore.
Um, swimming in the lakes is really nice, though
Feel free to PM me if you'd like more detail off-board.