I suspect a major reason is that they weren't going straight from the factory to the bomb racks. The empty casings may have been in outdoor storage until filled, then the filled bombs would be stacked and stored in the open on rail cars, in depots, and at the airfields. Unlike aluminum airplanes, too, bombs would have steel casings, and so be very prone to rust if not painted.
The two main reasons USAAF airplanes weren't painted starting in about 1943 were for weight savings (minimal for bombs which would only be making half the trip, anyway) and to save on man hours during construction (also minimal when you're talking about very simple bomb shapes).
The British military wasn't as keen on not following regulations when it was convenient as the US seemed to be. Considering that the British Army was repainting nearly all US vehicles from Olive Drab to Khaki Green No. 3 up until April 1944, I don't see the RAF abandoning bomb painting even if they were going almost straight from the factory to the bombers (which I doubt). I know a lot of British bombs were actually made in Canada and shipped across the Atlantic.
As I see it, that had to be a major factor. Even if you were making the bombs in the UK, I doubt the factory would know whether or not the bombs were being shipped to the nearest airfield, Italy, Africa, or India. For that reason, it was probably easiest to just paint all of them, than it was to not paint some of them and worry about whether or not some bombs were painted and some weren't, etc.