Getting rid of mold in areas you cannot reach
Although Vinigar is a weak acid it can kill surface mold. I would recommend hydrogen peroxide at 3% it is more effective at killing mold and bacteria and doesn't stink after application.
I would also spray the exposed wood surfaces, when lumber is milled it is sprayed with a biocide that doesn't last long and I have seen older units start to grow mushrooms in just a few months. And ply wood is worse when the sheets of veneer are cut mushrooms begin growing in days. Most spores are killed in the hot press process. Keeping the basement dry with a dehumidifier will be the best plan forward without moisture it cannot grow. But make sure to treat the exposed wood because you sleeping in that area create a large amount of exhaled moisture that may be enough to activate the mold.