I am not sure your expectations for distance. We used to walk on the internal park roads every day and we could walk 30 - 45 minutes in relatively flat terrain no retracing our route. Biking would be too short internally. There are back roads where the traffic speed are less that 70 mph but we never did this since we found the risks unacceptable. If you are willing to re-ride roads the internal roads could give you a good 5 mile ride. We stayed there 4 seasons and there are Escapees events and weekly meetings.

Providence Road runs between the RV side and permanent side where the Escapees HQ is. Connects to other roads, might be a good option for biking. I'd ask the locals in the park for more info. The main road (Hwy 146) has a 70 mph speed limit and almost no shoulders.