Have never driven anywhere with a road bike, but have taken my mtb with semi-slick tyres in the car to Mickleover and cycled the Pennine Bridleway (sustrans 68?) to Ashbourne. It starts with a 3 mile ride along an old railway line and then country lanes the rest of the way. It probably depends on what your road bike is like as to whether it’s rideable or not. I wouldn’t do it on something racey, but something like a Specialized Roubaix would be fine. You don’t see much traffic. It is out and back though.
Are you Coalville area? From there we used to do Heather – Market Bosworth – Twycross – Packington and back. I think that was about 30 miles. Also, Belton – Hathern – Sutton Bonnington – Kegworth then out to Sawley via Long Lane – Castle Donington and then back via Diseworth. That is a pretty flat route.