This has actually been tested, but results were not particularly positive.
During the Vietnam era, B-52s were painted with an "SEA" (South East Asia) camouflage scheme, which was black on the bottom, and fairly light green/brown colors on top:
During the cold war, the SEA camouflage scheme was replaced with the SIOP (Strategic Interdiction Operations Plan). The SIOP camouflage scheme for the B-52 had the bottom of the aircraft painted glossy white, and the top side in darker, flat colors (not black, but fairly dark greens and browns).
This picture looks pretty faded to me though--in real life, the top side was rather darker than shown here.
Around the mid-to-late 1980s, the SIOP camouflage scheme was replaced with the "new strategic" camouflage scheme, which was lighter grey, with minimal contrast between top and bottom (sorry, I haven't been able to chase down a picture of this one).
I never heard even the slightest suggestion that there might be even a slight difference in fuel usage depending on the camouflage scheme in use. It certainly wasn't mentioned in the documentation ("technical orders") and I never heard a pilot or navigator say anything even hinting at such a possibility either.
At least as I see things, the basic problem here is pretty simple. During a typical flight, you have an air speed in the range of hundreds of miles per hour, and you're typically flying in air that's at -40 degrees (or colder), so it's next to impossible for the light falling on the aircraft to heat it up to any noticeable degree at all.
In the specific case of a B-52 (or other strategic bomber) you do have the possibility of flying at terrain avoidance level (low altitude, so the air isn't nearly as cold), and you might be flying at somewhat lower speed, but your air speed is still going to be in the range of hundreds of miles per hour so you still have almost no possibility for light falling on the plane to raise its temperature to any significant degree. In any case, most aircraft don't fly at terrain avoidance level anyway.