Worth noting that the mushroom itself is just a temporary reproductive organ that's produced by the actual "body" of the fungus, which is a mycelial network spread through the soil. In this case the soil that's under that concrete. There must be a fair bit of organic matter in that soil, that's what the mushroom is feeding on.
Bleaching and cleaning the floor is fine, but it's probably not going to seep into the soil under there so next time the fungus down below has gathered up enough nutrients to be feeling randy again it'll just poke a new mushroom up through a crack. The cracks are probably just too fine to see. Maybe one solution might be to give the floor a really good scrubbing and cleaning, then once it dries spread some sealant on it? It'll hopefully seep into the cracks and make it harder for future intrusions.